bluuebunny/crossref_metadata_2025 huggingface dataset:
Estimating the Pool of Mobile Phosphorus in Offshore Soft Sediments of the Baltic Proper
Authors: Malmaeus J. Mikael , Karlsson O. Magnus
Published: December 2011

Background

Eutrophication is a major threat to many coastal ecosystems worldwide. This paper deals with the sediment-water exchange of phosphorus, one of the elements that may stimulate primary production in the aquatic environment. The lack of phosphorus-binding capacity in sediments at low redox-potential is recognized as an important mechanism for eutrophication-related effects in some areas.

Methods

Twelve sediment cores were collected in the Baltic Proper between 61 m and 175 m water depth and a number of phosphorus fractions were analyzed. Integrating the concentrations over the depth profiles, the amounts of mobile phosphorus were estimated in each core.

Results

It was found that sediments below the redox cline in the Baltic Proper contained small amounts of mobile phosphorus. The total amount of mobile phosphorus in the entire Baltic Proper sediments below 65 m water depth was estimated to between 55,000 tonnes and 156,000 tonnes or between less than 10% to around 25% of the phosphate in the system (water plus sediments). This represents the maximum amount of phosphorus that could possibly be released to the water column from these areas. We argue that the most reasonable estimate of the pool of mobile phosphorus in the sediments is the lower number.

Conclusion

The amounts of mobile phosphorus in sediment cores with oxidized surface layers were higher compared with sediment cores with reduced surfaces, indicating that there is a potential phosphorus-binding capacity in sediments below the redox cline if oxic conditions improved. Oxygenation of the Baltic Proper bottom water between 65 m and 100 m could probably remove around 100,000 tonnes of phosphorus from the water column and reduce phosphorus concentrations in the deep water by on average 30 mg/m3, which would possibly be felt also in the surface water.
Moyenne de localisation fréquentielle des paquets d'ondelettes
Authors: Fan Ai Hua
Published: December 2011

En utilisant le théorème de Ruelle d'opérateur de transfert, nous démontrons que la moyenne

2^{–k} \sum^{2^k–1}_{n=0} \parallel \hat {\omega}_n \parallel_{L^1}

de la localisation fréquentielle pour les paquets d'ondelettes admet un équivalent de la forme

c \rho ^k (c > 0, 1 < \rho < \sqrt 2)

. Cela améliore une inégalité antérieurement obtenue par Coifman, Meyer et Wickerhauser. Des estimations numériques de

\rho

sont obtenues pour des filtres de Daubechies.
Average decay of Fourier transforms and geometry of convex sets
Authors: Brandolini Luca , Rigoli Marco , Travaglini Giancarlo
Published: December 2011

Let

B

be a convex body in

\mathbb R^2

with piecewise smooth boundary and let

\widehat {\chi}_B

denote the Fourier transform of its characteristic function. In this paper we determine the admissible decays of the spherical

L^p

-averages of

\widehat {\chi}_B

and we relate our analysis to a problem in the geometry of convex sets. As an application we obtain sharp results on the average number of integer lattice points in large bodies randomly positioned in the plane.
The angular distribution of mass by Bergman functions
Authors: Marshall Donald E. , Smith Wayne
Published: December 2011

Let

\mathbb D = {z : |z| < 1}

be the unit disk in the complex plane and denote by

d\mathcal A

two-dimensional Lebesgue measure on

\mathbb D

. For

\epsilon > 0

we define

\sum_\epsilon = z:|

arg

z | < \epsilon

. We prove that for every

\epsilon > 0

there exists a

\delta > 0

such that if

f

is analytic, univalent and area-integrable on

\mathbb D

, and

f(0) = 0

, then

\int _{f^–1(\sum_\epsilon)} | f | d\mathcal A > \delta \int_\mathbb D | f | d\mathcal A

. This problem arose in connection with a characterization by Hamilton, Reich and Strebel of extremal dilatations for quasiconformal homeomorphisms of

\mathbb D

.
A Lieb-Thirring bound for a magnetic Pauli Hamiltonian, II
Authors: Bugliaro Luca , Fefferman Charles , Graf Gian Michele
Published: December 2011

We establish a Lieb-Thirring type estimate for Pauli Hamiltonians with nonhomogeneous magnetic fields. Besides of depending on the size of the field the bound also takes into account the size of the field gradient. We then apply the inequality to prove stability of non-relativistic quantum mechanical matter coupled to the quantized ultraviolet-cutoff electromagnetic field for arbitrary values of the fine structure constant.
On proximity relations for valuations dominating a two-dimensional regular local ring
Authors: Aparicio José Juan , Granja Ángel , Sánchez-Giralda Tomás
Published: December 2011

The purpose of this paper is to define a new numerical invariant of valuations centered in a regular two-dimensional regular local ring. For this, we define a sequence of non-negative rational numbers

\delta_\nu = \lbrace \delta_\nu (j)\rbrace_{j≥0}

which is determined by the proximity relations of the successive quadratic transformations at the points determined by a valuation

\nu

. This sequence is characterized by seven combinatorial properties so that any sequence of non-negative rational numbers having the above properties is the sequence associated to a valuation.
Evolution d'une singularité de type cusp dans une poche de tourbillon
Authors: Danchin Raphaël
Published: December 2011

We investigate the evolution of singularities in the boundary of a vortex patch for two-dimensional incompressible Euler equations. We are particularly interested in cusp-like singularities which, according to numerical simulations, are stable. In this paper, we first prove that, unlike the case of a corner-like singularity, the cusp-like singularity generates a lipschitzian velocity. We then state a global result of persistence of conformal regularity with respect to vector fields vanishing at a singular point, which generalizes the structure of cusp. This entails the stability of cusp-like structures for all time with conservation of the order of the cusp.

Dans cet article, on étudie l'évolution de singularités dans la frontière de poches de tourbillon pour les équations de la mécanique des fluides incompressible en dimension deux. On s'intéresse en particulier aux singularités de type cusp qui, d'après des simulations numériques réecentes, semblent stables.

On prouve ici que le champ de vitesse engendré par une poche de tourbillon ayant un cusp est lipschitzien (ce qui n'est pas le cas pour une singularité de type coin par exemple). On établit alors un résultat de persistance globale en temps d'un certain type de régularité conormale du tourbillon par rapport à une famille de champs de vecteurs s'annulant en un point singulier et qui généralise la structure de cusp.

On en déduit en particulier la stabilité pour tout temps du cusp avec conservation de l'ordre d'effilement.
On nonisometric isospectral connected fractal domains
Authors: Sleeman Brian D. , Chen Hua
Published: December 2011

A fundamental question raised by M. Kac in 1966 is: Must two isospectral planar domains necessarily be isometric? Following a long history of investigation C. Gordon, D. L. Webb and S. Wolpert in 1992 finally proved that the answer is no. By using the idea of transposition maps one can construct a wide class of planar domains with piecewise continuous boundaries which are isospectral but nonisometric. In this note we study the Kac question in relation to domains with fractal boundaries and by following a technique of paper folding maps by J. Chapman 1993 we construct pairs of isospectral but nonisometric connected planar domains with fractal boundaries having the same Minkowski dimension.
Paraproduit sur le groupe de Heisenberg et applications
Authors: Bahouri Hajer , Gallagher Isabelle
Published: December 2011

We adapt the homogeneous Littlewood–Paley decomposition on the Heisenberg group constructed by H. Bahouri, P. Gérard and C.-J Xu in [4] to the inhomogeneous case, which enables us to build paraproduct operators, similar to those defined by J.-M. Bony in [5]; although there is no simple formula for the Fourier transform of the product of two functions, some spectral localization properties of the classical case are preserved on the Heisenberg group after the product has been taken. Using the dyadic decomposition and the paraproduct algorithm, we prove the Gagliardo–Nirenberg inequality on the Heisenberg group; the smoothness of solutions of subelliptic, semi-linear systems is also studied, as well as semi-linear wave equations.

En adaptant au cas inhomogène la décomposition de Littlewood–Paley homogène sur le groupe de Heisenberg introduite par H. Bahouri, P. Gérard et C.-.J Xu dans [4] on construit des opérateurs de paraproduit analogues à ceux définis par J.-.M Bony dans [5]; malgré le fait que l'on ne dispose pas de formule simple pour la transformée de Fourier d'un produit des propriétés de localisation spectrale du cas classique sont préservées sur le groupe de Heisenberg après passage au produit. A partir du découpage dyadique et du paraproduit on démontre l'inégalité de Gagliardo–Nirenberg sur le groupe de Heisenberg et l'on étudie la régularité des solutions de systèmes sous-elliptiques semi-linéaires ainsi que des équations d'ondes semi-linéaires.
On certain Markov processes attached to exponential functionals of Brownian motion; application to Asian options
Authors: Donati-Martin Catherine , Ghomrasni Raouf , Yor Marc
Published: December 2011

We obtain a closed formula for the Laplace transform of the first moment of certain exponential functionals of Brownian motion with drift, which gives the price of Asian options. The proof relies on an identity in law between the average on [0,

t

] of a geometric Brownian motion and the value at time

t

of a Markov process for which we can compute explicitly the resolvent.
On pseudospheres that are quasispheres
Authors: Vogel Andrew , Lewis John L.
Published: December 2011

We construct bounded domains

D

not equal to a ball in

n≥3

dimensional Euclidean space,

\mathbb{R}^n

, for which

D

is homeomorphic to a sphere under a quasiconformal mapping of

\mathbb{R}^n

and such that

n-1

dimensional Hausdorff measure equals harmonic measure on

\partial D

.
Branching process associated with 2d-Navier Stokes equation
Authors: Benachour Saïd , Roynette Bernard , Vallois Pierre
Published: December 2011

\Omega

being a bounded open set in

\mathbb R^2

, with regular boundary, we associate with Navier–Stokes equation in

\Omega

where the velocity is null on

∂Ω

, a non-linear branching process (

Y_t; t ≥ 0

). More precisely:

E_{ω0} (h,Y_t) = (ω, h)

, for any test function

h

, where

ω = \mathrm{rot} u

,

u

denotes the velocity solution of Navier–Stokes equation. The support of the random measure

Y_t

increases or decreases of one unit when the underlying process hits

∂Ω

; this stochastic phenomenon corresponds to the creation-annihilation of vortex localized at the boundary of

Ω

.
Translation averages of dyadic weights are not always good weights
Authors: Ward Lesley A.
Published: December 2011

The process of translation averaging is known to improve dyadic BMO to the space BMO of functions of bounded mean oscillation, in the sense that the translation average of a family of dyadic BMO functions is necessarily a BMO function. The present work investigates the effect of translation averaging in other dyadic settings. We show that translation averages of dyadic doubling measures need not be doubling measures, translation averages of dyadic Muckenhoupt weights need not be Muckenhoupt weights, and translation averages of dyadic reverse Hölder weights need not be reverse Hölder weights. All three results are proved using the same construction.
Carleson measures for analytic Besov spaces
Authors: Arcozzi Nicola , Rochberg Richard , Sawyer Eric T.
Published: December 2011

We characterize Carleson measures for the analytic Besov spaces. The problem is first reduced to a discrete question involving measures on trees which is then solved. Applications are given to multipliers for the Besov spaces and to the determination of interpolating sequences. The discrete theorem is also applied to analysis of function space on trees.
Quasiconformal mappings of $Y$-pieces
Authors: Bishop Christopher J.
Published: December 2011

In this paper we construct quasiconformal mappings between Y-pieces so that the corresponding Beltrami coefficient has exponential decay away from the boundary. These maps are used in a companion paper to construct quasiFuchsian groups whose limit sets are non-rectifiable curves of dimension 1.
Lebesgue points for Sobolev functions on metric spaces
Authors: Kinnunen Juha , Latvala Visa
Published: December 2011

Our main objective is to study the pointwise behaviour of Sobolev functions on a metric measure space. We prove that a Sobolev function has Lebesgue points outside a set of capacity zero if the measure is doubling. This result seems to be new even for the weighted Sobolev spaces on Euclidean spaces. The crucial ingredient of our argument is a maximal function related to discrete convolution approximations. In particular, we do not use the Besicovitch covering theorem, extension theorems or representation formulas for Sobolev functions.
Global existence for the discrete diffusive coagulation-fragmentation equations in $L^1$
Authors: Laurençot Philippe , Mischler Stéphane
Published: December 2011

Existence of global weak solutions to the discrete coagulation-fragmentation equations with diffusion is proved under general assumptions on the coagulation and fragmentation coefficients. Unlike previous works requiring

L^\infty

-estimates, an

L^1

-approach is developed here which relies on weak and strong compactness methods in

L^1

.
Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms
Authors: Bonami Aline , Demange Bruno , Jaming Philippe
Published: December 2011

We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions

f

on

\mathbb{R}^d

which may be written as

P(x)\exp (-\langle Ax, x\rangle)

, with

A

a real symmetric definite positive matrix, are characterized by integrability conditions on the product

f(x) \widehat{f}(y)

. We then obtain similar results for the windowed Fourier transform (also known, up to elementary changes of functions, as the radar ambiguity function or the Wigner transform). We complete the paper with a sharp version of Heisenberg's inequality for this transform.
Mapping properties of the elliptic maximal function
Authors: Erdoğan M. Burak
Published: December 2011

We prove that the elliptic maximal function maps the Sobolev space

W_{4,\eta}(\mathbb{R}^2)

into

L^4(\mathbb{R}^2)

for all

\eta>1/6

. The main ingredients of the proof are an analysis of the intersection properties of elliptic annuli and a combinatorial method of Kolasa and Wolff.
Integral Closure of Monomial Ideals on Regular Sequences
Authors: Kiyek Karlheinz , Stückrad Jürgen
Published: December 2011

It is well known that the integral closure of a monomial ideal in a polynomial ring in a finite number of indeterminates over a field is a monomial ideal, again. Let

R

be a noetherian ring, and let

(x_1,\ldots,x_d)

be a regular sequence in

R

which is contained in the Jacobson radical of

R

. An ideal

\mathfrak a

of

R

is called a monomial ideal with respect to

(x_1,\ldots,x_d)

if it can be generated by monomials

x_1^{i_1}\cdots x_d^{i_d}

. If

x_1R+\cdots + x_dR

is a radical ideal of

R

, then we show that the integral closure of a monomial ideal of

R

is monomial, again. This result holds, in particular, for a regular local ring if

(x_1,\ldots,x_d)

is a regular system of parameters of

R

.
Modular Deformations and Space Curve Singularities
Authors: Martin Bernd
Published: December 2011

We investigate different concepts of modular deformations of germs of isolated singularities (infinitesimal, Artinian, formal). An obstruction calculus based on the graded Lie algebra structure of the tangent cohomology for modular deformations is introduced. As the main result the characterisation of the maximal infinitesimally modular subgerm of the miniversal family as flattening stratum of the relative Tjurina module is extended from ICIS to space curve singularities.
Local and Global Theory of the Moduli of Polarized Calabi-Yau Manifolds
Authors: Todorov Andrey
Published: December 2011

In this paper we review the moduli theory of polarized CY manifolds. We briefly sketched Kodaira–Spencer–Kuranishi local deformation theory developed by the author and G. Tian. We also construct the Teichmüller space of polarized CY manifolds following the ideas of I. R. Shafarevich and I. I. Piatetski–Shapiro. We review the fundamental result of E. Viehweg about the existence of the course moduli space of polarized CY manifolds as a quasi-projective variety. Recently S. Donaldson computed the moment map for the action of the group of symplectic diffeomorphisms on the space of Kähler metrics with fixed class of cohomology. Combining this results with the solution of Calabi conjecture by Yau one obtain a very conceptual proof of the existence of the coarse moduli space for a large class of varieties. We follow the approach developed in [24] to study the global properties of the moduli of polarized CY manifolds. We discuss the latest results connecting the discriminant locus in the moduli space of polarized odd dimensional CY manifolds with the Bismut–Gillet–Soule–Quillen–Donaldson Theory of Determinant line bundles.
Analysis of the free boundary for the $p$-parabolic variational problem $(p\ge 2)$
Authors: Shahgholian Henrik
Published: December 2011

Variational inequalities (free boundaries), governed by the

p

-parabolic equation (

p\geq 2

), are the objects of investigation in this paper. Using intrinsic scaling we establish the behavior of solutions near the free boundary. A consequence of this is that the time levels of the free boundary are porous (in

N

-dimension) and therefore its Hausdorff dimension is less than

N

. In particular the

N

-Lebesgue measure of the free boundary is zero for each

t

-level.
Mappings of finite distortion: Sharp Orlicz-conditions
Authors: Kauhanen Janne , Koskela Pekka , Malý Jan , Onninen Jani , Zhong Xiao
Published: December 2011

We establish continuity, openness and discreteness, and the condition

(N)

for mappings of finite distortion under minimal integrability assumptions on the distortion.
Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk
Authors: Poggi-Corradini Pietro
Published: December 2011

A lot is known about the forward iterates of an analytic function which is bounded by

1

in modulus on the unit disk

\mathbb{D}

. The Denjoy-Wolff Theorem describes their convergence properties and several authors, from the 1880's to the 1980's, have provided conjugations which yield very precise descriptions of the dynamics. Backward-iteration sequences are of a different nature because a point could have infinitely many preimages as well as none. However, if we insist in choosing preimages that are at a finite hyperbolic distance each time, we obtain sequences which have many similarities with the forward-iteration sequences, and which also reveal more information about the map itself. In this note we try to present a complete study of backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk.
Some nonexistence results for positive solutions of elliptic equations in unbounded domains
Authors: Damascelli Lucio , Gladiali Francesca
Published: December 2011

We prove some Liouville type theorems for positive solutions of semilinear elliptic equations in the whole space

\mathbb{R}^N

,

N\geq 3

, and in the half space

\mathbb{R}^N_{+}

with different boundary conditions, using the technique based on the Kelvin transform and the Alexandrov-Serrin method of moving hyperplanes. In particular we get new nonexistence results for elliptic problems in half spaces satisfying mixed (Dirichlet-Neumann) boundary conditions.
Endpoint estimates from restricted rearrangement inequalities
Authors: Carro María Belén J. , Martín Joaquim
Published: December 2011

Let

T

be a sublinear operator such that

(Tf)^*(t)\le h(t, \|f\|_1)

for some positive function

h(t,s)

and every function

f

such that

\|f\|_{\infty}\le 1

. Then, we show that

T

can be extended continuously from a logarithmic type space into a weighted weak Lorentz space. This type of result is connected with the theory of restricted weak type extrapolation and extends a recent result of Arias-de-Reyna concerning the pointwise convergence of Fourier series to a much more general context.
Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations
Authors: Kolokol'tsov Vassili N. , Schilling René L. , Tyukov Alexei E.
Published: December 2011

We study stochastic Hamilton-Jacobi-Bellman equations and the corresponding Hamiltonian systems driven by jump-type Lévy processes. The main objective of the present paper is to show existence, uniqueness and a (locally in time) diffeomorphism property of the solution: the solution trajectory of the system is a diffeomorphism as a function of the initial impulse. This result enables us to implement a stochastic version of the classical method of characteristics for the Hamilton-Jacobi equations. An -in itself interesting- auxiliary result are pointwise a.s. estimates for iterated stochastic integrals driven by a vector of not necessarily independent jump-type semimartingales.
Optimal Orlicz-Sobolev embeddings
Authors: Cianchi Andrea
Published: December 2011

An embedding theorem for the Orlicz-Sobolev space

W^{1,A}_{0}(G)

,

G\subset \mathbb{R}^n

, into a space of Orlicz-Lorentz type is established for any given Young function

A

. Such a space is shown to be the best possible among all rearrangement invariant spaces. A version of the theorem for anisotropic spaces is also exhibited. In particular, our results recover and provide a unified framework for various well-known Sobolev type embeddings, including the classical inequalities for the standard Sobolev space

W^{1,p}_{0}(G)

by O'Neil and by Peetre (

1\leq p< n

), and by Brezis-Wainger and by Hansson (

p=n

).
Approximation and symbolic calculus for Toeplitz algebras on the Bergman space
Authors: Suárez Daniel
Published: December 2011

If

f\in L^\infty(\mathbb{D})

let

T_f

be the Toeplitz operator on the Bergman space

L^2_a

of the unit disk

\mathbb{D}

. For a

C^\ast

-algebra

A\subset L^\infty(\mathbb{D})

let

\mathfrak{T}(A)

denote the closed operator algebra generated by

\{ T_f : f\in A \}

. We characterize its commutator ideal

\mathfrak C(A)

and the quotient

\mathfrak{T}(A)/ \mathfrak{C}(A)

for a wide class of algebras

A

. Also, for

n\geq 0

integer, we define the

n

-Berezin transform

B_nS

of a bounded operator

S

, and prove that if

f\in L^\infty(\mathbb{D})

and

f_n = B_n T_f

then

T_{f_n} \rightarrow T_f

.
Maximal real Schottky groups
Authors: Hidalgo Rubén A.
Published: December 2011

Let

S

be a real closed Riemann surfaces together a reflection

\tau:S \to S

, that is, an anticonformal involution with fixed points. A well known fact due to C. L. May [19] asserts that the group

K(S,\tau)

, consisting on all automorphisms (conformal and anticonformal) of

S

which commutes with

\tau

, has order at most

24(g-1)

. The surface

S

is called maximally symmetric Riemann surface if

|K(S,\tau)|=24(g-1)

[8]. In this note we proceed to construct real Schottky uniformizations of all maximally symmetric Riemann surfaces of genus

g \leq 5

. A method due to Burnside [3] permits us the computation of a basis of holomorphic one forms in terms of these real Schottky groups and, in particular, to compute a Riemann period matrix for them. We also use this in genus 2 and 3 to compute an algebraic curve representing the uniformized surface

S

. The arguments used in this note can be programed into a computer program in order to obtain numerical approximation of Riemann period matrices and algebraic curves for the uniformized surface

S

in terms of the parameters defining the real Schottky groups.
Focusing of spherical nonlinear pulses in ${\mathbb R}^{1+3}$, II. Nonlinear caustic
Authors: Carles Rémi , Rauch Jeffrey
Published: December 2011

We study spherical pulse like families of solutions to semilinear wave equations in space time of dimension 1+3 as the pulses focus at a point and emerge outgoing. We emphasize the scales for which the incoming and outgoing waves behave linearly but the nonlinearity has a strong effect at the focus. The focus crossing is described by a scattering operator for the semilinear equation, which broadens the pulses. The relative errors in our approximate solutions are small in the

L^\infty

norm.
Codimension one symplectic foliations
Authors: Calvo-Andrade Omegar , Muñoz Vicente , Presas Francisco
Published: December 2011

We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.
Minimal Slant Submanifolds of the smallest dimension in $S$-manifolds
Authors: Carriazo Alfonso , Fernández Luis M. , Hans-Uber María Belén
Published: December 2011

We study slant submanifolds of

S

-manifolds with the smallest dimension, specially minimal submanifolds and establish some relations between them and anti-invariant submanifolds in

S

-manifolds, similar to those ones proved by B.-Y. Chen for slant surfaces and totally real surfaces in Kaehler manifolds.
A note on the existence of $H$-bubbles via perturbation methods
Authors: Felli Veronica
Published: December 2011

We study the problem of existence of surfaces in

\mathbb{R}^3

parametrized on the sphere

{\mathbb S}^2

with prescribed mean curvature

H

in the perturbative case, i.e. for

H=H_0+\varepsilon H_1

, where

H_0

is a nonzero constant,

H_1

is a

C^2

function and

\varepsilon

is a small perturbation parameter.
Some Remarks on the Weak Maximum Principle
Authors: Rigoli Marco , Salvatori Maura , Vignati Marco
Published: December 2011

We obtain a maximum principle at infinity for solutions of a class of nonlinear singular elliptic differential inequalities on Riemannian manifolds under the sole geometrical assumptions of volume growth conditions. In the case of the Laplace-Beltrami operator we relate our results to stochastic completeness and parabolicity of the manifold.
Dyadic BMO on the bidisk
Authors: Blasco Óscar , Pott Sandra
Published: December 2011

We give several new characterizations of the dual of the dyadic Hardy space

H^{1,d}(\mathbb{T}^2)

, the so-called dyadic BMO space in two variables and denoted

\mathrm{BMO}^{\mathit d}_{\mathrm{prod}}

.
These include characterizations in terms of Haar multipliers, in terms of the “ymmetrised paraproduct”

\Lambda_b

, in terms of the rectangular BMO norms of the iterated “weeps”, and in terms of nested commutators with dyadic martingale transforms. We further explore the connection between

\mathrm{BMO}^{\mathit d}_{\mathrm{prod}}

and John–Nirenberg type inequalities, and study a scale of rectangular BMO spaces.
A Generalized Sharp Whitney Theorem for Jets
Authors: Fefferman Charles
Published: December 2011

Suppose that, for each point

x

in a given subset

E \subset \mathbb{R}^n

, we are given an

m

-jet

f(x)

and a convex, symmetric set

\sigma(x)

of

m

-jets at

x

. We ask whether there exist a function

F \in C^{m , \omega} ( \mathbb{R}^n )

and a finite constant

M

, such that the

m

-jet of

F

at

x

belongs to

f ( x ) + M \sigma ( x )

for all

x \in E

. We give a necessary and sufficient condition for the existence of such

F , M

, provided each

\sigma(x)

satisfies a condition that we call "Whitney

\omega

-convexity''.
Logarithmic derivative of the Euler $\Gamma$-function in Clifford analysis
Authors: Laville Guy , Randriamihamison Louis
Published: December 2011

The logarithmic derivative of the

\Gamma

-function, namely the

\psi

-function, has numerous applications. We define analogous functions in a four dimensional space. We cut lattices and obtain Clifford-valued functions. These functions are holomorphic cliffordian and have similar properties as the

\psi

-function. These new functions show links between well-known constants: the Euler gamma constant and some generalisations,

\zeta^R(2)

,

\zeta^R(3)

. We get also the Riemann zeta function and the Epstein zeta functions.
Potential Theory for Schrödinger operators on finite networks
Authors: Bendito Enrique , Carmona Ángeles , Encinas Andrés M.
Published: December 2011

We aim here at analyzing the fundamental properties of positive semidefinite Schrödinger operators on networks. We show that such operators correspond to perturbations of the combinatorial Laplacian through 0-order terms that can be totally negative on a proper subset of the network. In addition, we prove that these discrete operators have analogous properties to the ones of elliptic second order operators on Riemannian manifolds, namely the monotonicity, the minimum principle, the variational treatment of Dirichlet problems and the condenser principle. Unlike the continuous case, a discrete Schrödinger operator can be interpreted as an integral operator and therefore a discrete Potential Theory with respect to its associated kernel can be built. We prove that the Schrödinger kernel satisfies enough principles to assure the existence of equilibrium measures for any proper subset. These measures are used to obtain systematic expressions of the Green and Poisson kernels associated with Dirichlet problems.
Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials
Authors: Baranger Céline , Mouhot Clément
Published: December 2011

This paper deals with explicit spectral gap estimates for the linearized Boltzmann operator with hard potentials (and hard spheres). We prove that it can be reduced to the Maxwellian case, for which explicit estimates are already known. Such a method is constructive, does not rely on Weyl's Theorem and thus does not require Grad's splitting. The more physical idea of the proof is to use geometrical properties of the whole collision operator. In a second part, we use the fact that the Landau operator can be expressed as the limit of the Boltzmann operator as collisions become grazing in order to deduce explicit spectral gap estimates for the linearized Landau operator with hard potentials.
The bidual of a tensor product of Banach spaces
Authors: Cabello Sánchez Félix , García Ricardo
Published: December 2011

This paper studies the relationship between the bidual of the (projective) tensor product of Banach spaces and the tensor product of their biduals.
Fractional iteration in the disk algebra: prime ends and composition operators
Authors: Contreras Manuel D. , Díaz-Madrigal Santiago
Published: December 2011

In this paper we characterize the semigroups of analytic functions in the unit disk which lead to semigroups of operators in the disk algebra. These characterizations involve analytic as well as geometric aspects of the iterates and they are strongly related to the classical theorem of Carath\'eodory about local connection and boundary behaviour of univalent functions.
Generalized Hantzsche-Wendt flat manifolds
Authors: Rossetti Juan P. , Szczepański Andrzej
Published: December 2011

We study the family of closed Riemannian

n

-manifolds with holonomy group isomorphic to

\mathbb{Z}_2^{n-1}

, which we call generalized Hantzsche-Wendt manifolds. We prove results on their structure, compute some invariants, and find relations between them, illustrated in a graph connecting the family.
An extension of the Krein-Šmulian Theorem
Authors: Granero Antonio S.
Published: December 2011

Let

X

be a Banach space,

u\in X^{**}

and

K, Z

two subsets of

X^{**}

. Denote by

d(u,Z)

and

d(K,Z)

the distances to

Z

from the point

u

and from the subset

K

respectively. The Krein-Šmulian Theorem asserts that the closed convex hull of a weakly compact subset of a Banach space is weakly compact; in other words, every w

^*

-compact subset

K\subset X^{**}

such that

d(K,X)=0

satisfies

d(\overline{\text{co}}^{w^*}(K),X)=0

. We extend this result in the following way: if

Z\subset X

is a closed subspace of

X

and

K\subset X^{**}

is a w

^*-

compact subset of

X^{**}

, then

d(\overline{\text{co}}^{w^*}(K),Z)\leq 5 d(K,Z).

Moreover, if

Z\cap K

is w

^*

-dense in

K

, then

d(\overline{\text{co}}^{w^*}(K),Z)\leq 2 d(K,Z)

. However, the equality

d(K,X)=d(\overline{\text{co}}^{w^*}(K),X)

holds in many cases, for instance, if

\ell_1\not\subseteq X^*

, if

X

has w

^*

-angelic dual unit ball (for example, if

X

is WCG or WLD), if

X=\ell_1(I)

, if

K

is fragmented by the norm of

X^{**}

, etc. We also construct under

CH

a w

^*

-compact subset

K\subset B(X^{**})

such that

K\cap X

is w

^*

-dense in

K

,

d(K,X)=\frac 12

and

d(\overline{\text{co}}^{w^*}(K),X)=1

.
Super and ultracontractive bounds for doubly nonlinear evolution equations
Authors: Bonforte Matteo , Grillo Gabriele
Published: December 2011

We use logarithmic Sobolev inequalities involving the

p

-energy functional recently derived in [Del Pino, M. and Dolbeault, J.: The optimal euclidean

\mathrm{L}^p

-Sobolev logarithmic inequality. J. Funct. Anal. 197 (2003), 151–161], [Gentil, I.: The general optimal

\mathrm{L}^p

-Euclidean logarithmic Sobolev inequality by Hamilton-Jacobi equations. J. Funct. Anal. 202 (2003), 591–599] to prove L

^p

-L

^q

smoothing and decay properties, of supercontractive and ultracontractive type, for the semigroups associated to doubly nonlinear evolution equations of the form

\dot u=\triangle_p(u^m)

(with

(m(p-1)\ge 1

) in an arbitrary euclidean domain, homogeneous Dirichlet boundary conditions being assumed. The bounds are of the form

\Vert u(t)\Vert_q\le C\Vert u_0\Vert_r^\gamma/t^\beta

for any

r\le q\in[1,+\infty]

and

t>0

and the exponents

\beta,\gamma

are shown to be the only possible for a bound of such type.
On Clifford’s theorem for rank-3 bundles
Authors: Lange Herbert , Newstead Peter E.
Published: December 2011

In this paper we obtain bounds on

h^0(E)

where

E

is a semistable bundle of rank 3 over a smooth irreducible projective curve

X

of genus

g \geq 2

defined over an algebraically closed field of characteristic 0. These bounds are expressed in terms of the degrees of stability

s_1(E)

,

s_2(E)

. We show also that in some cases the bounds are best possible. These results extend recent work of J. Cilleruelo and I. Sols for bundles of rank 2.
On Hilbert modular forms modulo $p$: explicit ring structure
Authors: Nagaoka Shoyu
Published: December 2011

H.P.F. Swinnerton-Dyer determined the structure of the ring of modular forms modulo

p

in the elliptic modular case. In this paper, the structure of the ring of Hilbert modular forms modulo

p

is studied. In the case where the discriminant of corresponding quadratic field is 8 (or 5), the explicit structure is determined.
Arithmetic properties of positive integers with fixed digit sum
Authors: Luca Florian
Published: December 2011

In this paper, we look at various arithmetic properties of the set of those positive integers

n

whose sum of digits in a fixed base

b>1

is a fixed positive integers

s

. For example, we prove that such integers can have many prime factors, that they are not very smooth, and that most such integers have a large prime factor dividing the value of their Euler

\phi

function.
Superposition operators and functions of bounded $p$-variation
Authors: Bourdaud Gérard , Lanza de Cristoforis Massimo , Sickel Winfried
Published: December 2011

We characterize the set of all functions

f

of

\mathbb R

to itself such that the associated superposition operator

T_f: g \to f \circ g

maps the class

BV^1_p (\mathbb R)

into itself. Here

BV^1_p (\mathbb R)

,

1 \le p < \infty

, denotes the set of primitives of functions of bounded

p

-variation, endowed with a suitable norm. It turns out that such an operator is always bounded and sublinear. Also, consequences for the boundedness of superposition operators defined on Besov spaces

B^s_{p,q}({\mathbb R}^n)

are discussed.
$m$-Berezin transform and compact operators
Authors: Nam Kyesook , Zheng Dechao , Zhong Changyong
Published: December 2011

m

-Berezin transforms are introduced for bounded operators on the Bergman space of the unit ball. The norm of the

m

-Berezin transform as a linear operator from the space of bounded operators to

L^{\infty}

is found. We show that the

m

-Berezin transforms are commuting with each other and Lipschitz with respect to the pseudo-hyperbolic distance on the unit ball. Using the

m

-Berezin transforms we show that a radial operator in the Toeplitz algebra is compact iff its Berezin transform vanishes on the boundary of the unit ball.
Uniform Bounds for the Bilinear Hilbert Transforms, II
Authors: Li Xiaochun
Published: December 2011

We continue the investigation initiated in [Grafakos and Li: Uniform bounds for the bilinear Hilbert transforms, I. Ann. of Math. (2) 159 (2004), 889-933] of uniform

L^{p}

bounds for the family of bilinear Hilbert transforms

H_{\alpha,\beta} (f,g)(x) = \text{p.v.} \displaystyle\int_{\mathbb{R}} f(x-\alpha t) g(x-\beta t) \frac{dt}{t} \,.

In this work we show that

H_{\alpha,\beta}

map

L^{p_1}(\mathbb R)\times L^{p_2}(\mathbb R)

into

L^p(\mathbb R)

uniformly in the real parameters

\alpha

,

\beta

satisfying

|\frac{\alpha}{\beta}-1|\ge c > 0

when

1 < p_1, p_2 < 2

and

\frac{2}{3} < p= \frac{p_1p_2}{p_1+p_2} < \infty

. As a corollary we obtain

L^p \times L^\infty \to L^p

uniform bounds in the range

4/3 < p < 4

for the

H_{1,\alpha}

's when

\alpha\in [0,1)

.
Local Fatou theorem and the density of energy on manifolds of negative curvature
Authors: Mouton Frédéric
Published: December 2011

Let

u

be a harmonic function on a complete simply connected manifold

M

whose sectional curvatures are bounded between two negative constants. It is proved here a pointwise criterion of non-tangential convergence for points of the geometric boundary: the finiteness of the density of energy, which is the geometric analogue of the density of the area integral in the Euclidean half-space
Stability of Lewis and Vogel’s result
Authors: Preiss David , Toro Tatiana
Published: December 2011

Lewis and Vogel proved that a bounded domain whose Poisson kernel is constant and whose surface measure to the boundary has at most Euclidean growth is a ball. In this paper we show that this result is stable under small perturbations. In particular a bounded domain whose Poisson kernel is smooth and close to a constant, and whose surface measure to the boundary has at most Euclidean growth is a smooth deformation of a ball.
Nonvariational layer potentials with respect to H¨older continuous vector fields
Authors: Verchota Gregory C.
Published: December 2011

Nontangential a.e. vanishing of the oblique derivative of a harmonic function with respect to a Hölder continuous vector field on a Lipschitz boundary is shown to imply that the harmonic function is constant.
On the density of continuous functions in variable exponent Sobolev space
Authors: Hästö Peter
Published: December 2011

In this article we give new conditions for the density of continuous or smooth functions in variable exponent Sobolev spaces. Our first result combines the previously known sufficient conditions, a monotony condition by Edmunds and R#x00E1;kosn#x00ED;k and a continuity condition independently due to Samko and Diening, into a single weaker condition. The second main result gives a sufficient condition in terms of the regularity of the level-sets of the variable exponent.
Group actions on Jacobian varieties
Authors: Rojas Anita M.
Published: December 2011

Consider a finite group

G

acting on a Riemann surface

S

, and the associated branched Galois cover

\pi_G:S \to Y=S/G

. We introduce the concept of \emph{geometric signature} for the action of

G

, and we show that it captures much information: the geometric structure of the lattice of intermediate covers, the isotypical decomposition of the rational representation of the group

G

acting on the Jacobian variety

JS

of

S

, and the dimension of the subvarieties of the isogeny decomposition of

JS

. We also give a version of Riemann's existence theorem, adjusted to the present setting.
On the regularity of averages over spheres for kinetic transport equations in hyperbolic Sobolev spaces
Authors: Bournaveas Nikolaos , Gutiérrez Susana
Published: December 2011

We study the smoothing effect of averaging over spheres for solutions of kinetic transport equations in hyperbolic Sobolev spaces.
Properties of centered random walks on locally compact groups and Lie groups
Authors: Dungey Nick
Published: December 2011

The basic aim of this paper is to study asymptotic properties of the convolution powers

K^{(n)} = K*K* \cdots *K

of a possibly non-symmetric probability density

K

on a locally compact, compactly generated group

G

. If

K

is centered, we show that the Markov operator

T

associated with

K

is analytic in

L^p(G)

for

1 < p < \infty

, and establish Davies-Gaffney estimates in

L^2

for the iterated operators

T^n

. These results enable us to obtain various Gaussian bounds on

K^{(n)}

. In particular, when

G

is a Lie group we recover and extend some estimates of Alexopoulos and of Varopoulos for convolution powers of centered densities and for the heat kernels of centered sublaplacians. Finally, in case

G

is amenable, we discover that the properties of analyticity or Davies-Gaffney estimates hold only if

K

is centered.
A universal Lipschitz extension property of Gromov hyperbolic spaces
Authors: Brudnyi Alexander , Brudnyi Yuri
Published: December 2011

A metric space

U

has the universal Lipschitz extension property if for an arbitrary metric space

M

and every subspace

S

of

M

isometric to a subspace of

U

there exists a continuous linear extension of Banach-valued Lipschitz functions on

S

to those on all of

M

. We show that the finite direct sum of Gromov hyperbolic spaces of bounded geometry is universal in the sense of this definition.
Optimizing geometric measures for fixed minimal annulus and inradius
Authors: Hernández Cifre María A. , Herrero Piñeyro Pedro J.
Published: December 2011

In this paper we relate the minimal annulus of a planar convex body

K

with its inradius, obtaining all the upper and lower bounds, in terms of these quantities, for the classic geometric measures associated with the set: area, perimeter, diameter, minimal width and circumradius. We prove the optimal inequalities for each one of those problems, determining also its corresponding extremal sets.
Weak type estimates associated to Burkholder’s martingale inequality
Authors: Parcet Javier
Published: December 2011

Given a probability space

(\Omega, \mathsf{A}, \mu)

, let

\mathsf{A}_1, \mathsf{A}_2, \ldots

be a filtration of

\sigma

-subalgebras of

\mathsf{A}

and let

\mathsf{E}_1, \mathsf{E}_2, \ldots

denote the corresponding family of conditional expectations. Given a martingale

f = (f_1, f_2, \ldots)

adapted to this filtration and bounded in

L_p(\Omega)

for some

2 \le p < \infty

, Burkholder's inequality claims that

\|f\|_p \sim_{\mathrm{c}_p} \Big\| \Big( \sum_{k=1}^\infty \mathsf{E}_{k-1}(|df_k|^2) \Big)^\frac12 \Big\|_p + \Big( \sum_{k=1}^\infty \|df_k\|_p^p \Big)^\frac1p.

Motivated by quantum probability, Junge and Xu recently extended this result to the range

1 < p < 2

. In this paper we study Burkholder's inequality for

p=1

, for which the techniques must be different. Quite surprisingly, we obtain two non-equivalent estimates which play the role of the weak type

(1,1)

analog of Burkholder's inequality. As application we obtain new properties of Davis decomposition for martingales.
Transformations between surfaces in $\mathbb{R}^4$ with flat normal and/or tangent bundles
Authors: Montesinos-Amilibia Angel
Published: December 2011

We exhibit several transformations of surfaces

M

in

\mathbb{R}^4

: a transformation of flat surfaces that gives surfaces with flat normal bundle (semiumbilical surfaces); and its inverse that from a semiumbilical surface obtains a flat surface; then a one-parameter family of transformations

f

on flat semiumbilical immersed surfaces (FSIS), such that

df(T_pM)

is totally orthogonal to

T_pM,

and that give FSIS. This family satisfies a Bianchi type of permutability property.
A finiteness theorem for the space of $L^{p}$ harmonic sections
Authors: Pigola Stefano , Rigoli Marco , Setti Alberto G.
Published: December 2011

In this paper we give a unified and improved treatment to finite dimensionality results for subspaces of

L^{p}

harmonic sections of Riemannian or Hermitian vector bundles over complete manifolds. The geometric conditions on the manifold are subsumed by the assumption that the Morse index of a related Schr#x00F6;dinger operator is finite. Applications of the finiteness theorem to concrete geometric situations are also presented.
The algebro-geometric Toda hierarchy initial value problem for complex-valued initial data
Authors: Gesztesy Fritz , Holden Helge , Teschl Gerald
Published: December 2011

We discuss the algebro-geometric initial value problem for the Toda hierarchy with complex-valued initial data and prove unique solvability globally in time for a set of initial (Dirichlet divisor) data of full measure. To this effect we develop a new algorithm for constructing stationary complex-valued algebro-geometric solutions of the Toda hierarchy, which is of independent interest as it solves the inverse algebro-geometric spectral problem for generally non-self-adjoint Jacobi operators, starting from a suitably chosen set of initial divisors of full measure. Combined with an appropriate first-order system of differential equations with respect to time (a substitute for the well-known Dubrovin equations), this yields the construction of global algebro-geometric solutions of the time-dependent Toda hierarchy. The inherent non-self-adjointness of the underlying Lax (i.e., Jacobi) operator associated with complex-valued coefficients for the Toda hierarchy poses a variety of difficulties that, to the best of our knowledge, are successfully overcome here for the first time. Our approach is not confined to the Toda hierarchy but applies generally to

1+1

-dimensional completely integrable discrete soliton equations.
Sampling Sets for the Nevanlinna class
Authors: Massaneda Xavier , Thomas Pascal J.
Published: December 2011

We propose a definition of sampling set for the Nevanlinna and Smirnov classes in the disk and show its equivalence with the notion of determination set for the same classes. We also show the relationship with determination sets for related classes of functions and deduce a characterization of Smirnov sampling sets. For Nevanlinna sampling we give general conditions (necessary or sufficient), from which we obtain precise geometric descriptions in several regular cases.
Erratum: A Parabolic Quasilinear Problem for Linear Growth Functionals
Authors: Andreu Fuensanta , Caselles Vicent , Mazón José M.
Published: December 2011

We give the correct proof of Lemma 3.6 of the paper
A Parabolic Quasilinear Problem for Linear Growth Functionals
(Rev. Mat. Iberoamericana
18
(2002), no. 1, 135–185).
Geometric optics with critical vanishing viscosity for one-dimensional semilinear initial value problems
Authors: Junca Stéphane
Published: December 2011

We study the propagation of high frequency oscillations for one dimensional semi-linear hyperbolic systems with small parabolic perturbations. We obtain a new degenerate parabolic system for the profile, and valid an asymptotic development in the spirit of Joly, Métivier and Rauch.