rough singular integrals on triebel lizorkin space and besov space abstract in this paper the authors prove that the homogeneous singular integral t with h 1 s n 1 is bounded on the triebel lizorkin spaces and the besov spaces these results answer an open problem proposed by chen and zhang in j chen c zhang boundedness of rough singular integral on the triebel lizorkin spaces j math anal appl 337 2008 1048 1052 the same results hold also for the rough singular integral operators t h with radial function kernels

domain walls in the coupled gross pitaevskii equations a thorough study of domain wall solutions in coupled gross pitaevskii equations on the real line is carried out including existence of these solutions their spectral and nonlinear stability their persistence and stability under a small localized potential the proof of existence is variational and is presented in a general framework we show that the domain wall solutions are energy minimizers within a class of vector valued functions with nontrivial conditions at infinity the admissible energy functionals include those corresponding to coupled gross pitaevskii equations arising in modeling of bose einstein condensates the results on spectral and nonlinear stability follow from properties of the linearized operator about the domain wall the methods apply to many systems of interest and integrability is not germane to our analysis finally sufficient conditions for persistence and stability of domain wall solutions are obtained to show that stable pinning occurs near maxima of the potential thus giving rigorous justification to earlier results in the physics literature

improved stability robustness bounds using state transformation for linear discrete systems abstract sufficient condition bounds on the linear time varying perturbations for robust stability of an asymptotically stable linear time invariant discrete time system have been reported recently the development involves both schwartz and triangular inequalities and tends to give conservative results this paper uses state transformation to obtain improvement in these bounds both unstructured and structured perturbation bounds are shown to improve using transformations the proposed analysis is applied to a fourth order macroeconomic system model

a rough hypersingular integral operator with an oscillating factor abstract we study certain hypersingular integrals t f defined on all test functions f s r n where the kernel of the operator t has a strong singularity y n 0 at the origin an oscillating factor e i y 0 and a distribution h r s n 1 0 r 1 we show that t extends to a bounded linear operator from the sobolev space l p l p to the lebesgue space l p for p if the distribution is in the hardy space h r s n 1 with 0 r n 1 n 1 0 and 2 0

computer aided determination of stability robustness measure of linear discrete time systems abstract in this paper several upper bounds for parameter variations of a linear discrete time system that is expressed in either matrix or polynomial form are presented within these upper bounds the system remains asymptotically stable these upper bounds which are only a set of sufficient conditions are then used iteratively in a computer aided algorithm to reach to the largest numerical such upper bounds the largest numerical upper bound is called the stability robustness measure of the discrete time dynamic system

ell p left mathbb z d right estimates for discrete operators of radon type variational estimates we prove ell p left mathbb z d right bounds for p in 1 infty of r variations r in 2 infty for discrete averaging operators and truncated singular integrals of radon type we shall present a new powerful method which allows us to deal with these operators in a unified way and obtain the range of parameters of p and r which coincide with the ranges of their continuous counterparts

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

the hilbert transform and maximal function for approximately homogeneous curves let 9ckf x p v f i f x y t dt t and 6 yf x sup1 h 0 h f if x y t l dt it is proved that for f e i rn the schwartz class and for an approximately homogeneous curve y t e ri i ilyf 112 ciifii2 116xyfi12 s c11fi12a homogeneous curve is one which satisfies a differential equation y t a t y t 0 t oo where a is a nonsingular matrix all of whose eigenvalues have positive real part an approximately homogeneous curve y t has the form y1 t y2 t where y2 t is a carefully specified error such that 4yi is also restricted for 2 n 1 the approximately homogeneous curves generalize the curves of standard type treated by stein and wainger

lp boundedness of marcinkiewicz integral operators abstract in this paper we prove the l p boundedness of marcinkiewicz integral operators associated to compact submanifolds of finite type under the l log l 1 2 condition on the kernel functions the exponent 1 2 is optimal we also show that the l p boundedness may fail to hold if the underlying submanifold is not required to be of finite type

phase transition in a rabi coupled two component bose einstein condensate abstract this paper deals with the study of the phase transition of the wave functions of a segregated two component bose einstein condensate under rabi coupling this yields a system of two coupled ode s where the rabi coupling is linear in the other wave function and acts against segregation we prove estimates on the asymptotic behaviour of the wave functions as the strength of the interaction gets strong or weak we also derive limiting problems in both cases

jump estimates for operators associated with polynomials abstract in this study we prove the jump inequalities for singular integrals and averages of radon type with rough kernels

a maximal function for families of hilbert transforms along homogeneous curves let h u be the hilbert transform along the parabola t ut 2 where u in mathbb r for a set u of positive numbers consider the maximal function mathcal h u f sup h u f u in u we obtain an essentially optimal result for the l p operator norm of mathcal h u when 2 p infty the results are proved for families of hilbert transforms along more general nonflat homogeneous curves

uniform estimates for bilinear hilbert transforms and bilinear maximal functions associated to polynomials we study the bilinear hilbert transforms and bilinear maximal functions associated to non flat polynomial curves and obtain uniform l r estimates for r d 1 over d where d is the degree of the polynomial in addition the lower bound of r is sharp up to the end point

analysis and applications of robust nonsingularity problem using the structured singular value this note uses the structured singular value technique to solve the robust nonsingularity analysis problem for matrices with unstructured and or quadratically coupled structured uncertainties with the ready spl mu analysis tools a new approach is proposed for finding a set of uncertainties within which the perturbed matrix keeps nonsingularity applications and examples in robust control theory are given to show the usefulness and the practicality of the proposed approach

a degenerate isoperimetric problem and traveling waves to a bistable hamiltonian system we analyze a nonstandard isoperimetric problem in the plane associated with a metric having degenerate conformal factor at two points under certain assumptions on the conformal factor we establish the existence of curves of least length under a constraint associated with enclosed euclidean area as a motivation for and application of this isoperimetric problem we identify these isoperimetric curves appropriately parametrized as traveling wave solutions to a bistable hamiltonian system of pdes we also determine the existence of a maximal propagation speed for these traveling waves through an explicit upper bound depending on the conformal factor 2015 wiley periodicals inc

compactness for the commutators of singular integral operators with rough variable kernels abstract let t be the singular integral operator with variable kernel defined by t f x p v r n x x y x y n f y d y where x y is homogeneous of degree zero in the second variable y and s n 1 x z d z 0 for any x r n in this paper the authors prove that if l r n l q s n 1 for some q 2 n 1 n then the commutator generated by a cmo r n function and t and the associated lacunary maximal operator are compact on l 2 r n the associated continuous maximal commutator is also considered

a note on marcinkiewicz integral operators abstract this paper is primarily concerned with proving the l p boundedness of marcinkiewicz integral operators with kernels belonging to certain block spaces we also show the optimality of our condition on the kernel for the l 2 boundedness of the marcinkiewicz integral

weighted boundedness for rough marcinkiewicz integrals with different weights in this paper the authors give the weighted boundedness of the marcinkiewicz integral operators for different weight functions where the kernel functions of the operators discussed here are without smoothness not only on the sphere but also in the radial direction

singular integral operators with rough convolution kernels in all dimensions again under the assumption q e l log l it is conceivable that a variant of the arguments in 3 for the maximal operator could also work for the singular integral operator in fact in unpublished work the authors of 3 obtained a weak type 1 1 inequality in dimension d 7 however their arguments if applied to the singular integral operator lead to substantial technical difficulties and no

robust stability of state space models with structured uncertainties a method for robust eigenvalue location analysis of linear state space models affected by structured real parametric perturbations is proposed the approach based on algebraic matrix properties deals with state space models in which system matrix entries are perturbed by polynomial functions of a set of uncertain physical parameters a method converting the robust stability problem into nonsingularity analysis of a suitable matrix is proposed the method requires a check of the positivity of a multinomial form over a hyperrectangular domain in parameter space this problem which can be reduced to finding the real solutions of a system of polynomial equations simplifies considerably when cases with one or two uncertain parameters are considered for these cases necessary and sufficient conditions for stability are given in terms of the solution of suitable real eigenvalue problems

robustness analysis of uncertain linear singular systems with output feedback control the robustness analysis for a linear singular system with uncertain parameters and static output feedback control is considered the problem is transformed into a robust nonsingularity problem based on the linear fractional transformation lft approach the robustness bounds to preserve regularity impulse immunity and stability are found in terms of the structured singular value spl mu with respect to parametric uncertainties the lft approach provides a unified framework for robustness analysis of both uncertain linear continuous discrete time singular systems

harmonic analysis on product spaces rn x r and commute with the dilations p33 8 x2 x2 61x1 62x2 for x1 e rn x2 e rm and 61 82 0 then the corresponding operators are related to many problems in the theory of multiple fourier integrals see zygmund 21 the maximal operator which commutes with the p31382 is the jessen marcinkiewicz and zygmund 14 strong maximal operator ms defined by 1 ms f x1 x2 sup ri a y1 y2 1 dy1 dy2 xl x2 gr jr1

a note on a class of rough maximal operators on product domains abstract in this note we give thel2 r n r m boundedness of a class of maximal singular integral operators with kernel function inl log l 2 sn 1 sm 1

l p bounds for the commutators of singular integrals and maximal singular integrals with rough kernels the commutator of convolution type calderon zygmund singular integral operators with rough kernels p v x n are studied the authors established the l p 1 p boundedness of the commutators of singular integrals and maximal singular integrals with the kernel condition which is different from the condition h1 sn 1 mr 2000 subject classification 42b20 42b25 42b99

computation of nonconservative stability perturbation bounds for systems with nonlinearly correlated uncertainties consideration is given to the problem of robust stability analysis of linear dynamic systems with uncertain physical parameters entering as polynomials in the state equation matrices a method is proposed giving necessary and sufficient conditions for computing the uncertain system stability margin in parameter space which provides a measure of maximal parameter perturbations preserving stability of the perturbed system around a known stable nominal system a globally convergent optimization algorithm that enables solutions to the problem to be obtained is presented using the polynomial structure of the problem the algorithm generates a convergent sequence of interval estimates of the global extremum these intervals provide a measure of the accuracy of the approximating solution achieved at each step of the iterative procedure some numerical examples are reported showing attractive features of the algorithm from the point of view of computational burden and convergence behavior

boundedness for the commutator of convolution operator a boundedness result is established for sublinear operators on homogeneous herz spaces as applications a new result about the weighted boundedness of commutators of convolution operators is obtained

littlewood paley characterization and duality of weighted anisotropic product hardy spaces the authors study anisotropic product hardy spaces hwp a associated with a pair a a1 a2 of expansive dilations and a class of product muckenhoupt weights a a on rn rm this article is a continuation of their earlier work in bownik et al 2010 8 the authors establish the littlewood paley g function characterization and the transform characterization of hwp a 0 p 1 the authors also introduce the weighted anisotropic product campanato space lp w a and establish its transform characterization as an application the authors identify the dual space of hwp a with lp w a the results of this article improve the existing results for weighted product hardy spaces on r r and are new even in the weighted isotropic setting

rank preservation of matrices with structured uncertainties and its applications in robust control theory matrix rank is determined by the nonsingularity of its submatrices for matrices in which entries are quadratic functions of some uncertain parameters this paper derives sufficient conditions on parameters to that ensure the matrices preserve to some degrees the ranks they have when the parameters are all zero the rank preservation problem is converted to the nonsingularity analysis problem of the minors of the matrix in discussion and suitable tools such as the spl mu analysis method are used to solve the problem applications in robust control theory including tests for robust controllability observability minimum phaseness coprimeness and schur stability are given together with illustrative examples

stability theory of solitary waves in the presence of symmetry ii abstract consider an abstract hamiltonian system which is invariant under a group of operators we continue to study the effect of the group invariance on the stability of solitary waves applications are given to bound states and traveling wave solutions of nonlinear wave equations

maximal operators along surfaces of revolution in lebesgue mixed norm spaces in this paper we establish the boundedness of certain maximal operators along hyperspaces in lebesgue mixed norm spaces

singular integral operators on function spaces we study the singular integral operator fx t y f x ty defined on all test functions f w hereb is a bounded function 0 is suitable distribution on the unit sphere s n 1 satisfying some cancellation conditions we prove certain boundedness properties of t on the triebel lizorkin spaces and on the besov spaces we also use our results to study the littlewood paley functions these results improve and extend some well known results

maximal functions associated to surfaces of revolution on product domains abstract the author establishes the l p boundedness for a class of maximal functions related to singular integrals associated to surfaces of revolution on product domains with rough kernels in l log l s n 1

robust stability bounds on time varying perturbations for state space models of linear discrete time systems the stability robustness of linear discrete time systems in the time domain is addressed using the lyapunov approach bounds on linear time varying perturbations that maintain the stability of an asymptotically stable linear time invariant discrete time nominal system are obtained for both structured and unstructured independent perturbations bounds are also derived assuming that various elements of the system matrix are perturbed dependently the result for the structured perturbation case is extended to the stability analysis of interval matrices

rough maximal singular integral and maximal operators supported by subvarieties on triebel lizorkin spaces abstract in this paper our object of investigation is the maximal singular integrals with rough kernels associated to polynomial mapping p as well as the corresponding compound submanifolds which is defined by t h p f x sup 0 y f x p y h y y y n d y we show that the operator t h p is bounded on triebel lizorkin spaces and besov spaces when the rough kernel l log l s n 1 for some 0 1 similar results can be extended to hardy littlewood maximal operators with rough kernels associated to the mapping p

one modification of the martingale transform and its applications to paraproducts and stochastic integrals abstract in this paper we introduce a variant of burkholder s martingale transform associated with two martingales with respect to different filtrations even though the classical martingale techniques cannot be applied we show that the discussed transformation still satisfies some expected l p estimates then we apply the obtained inequalities to general dilation twisted paraproducts particular instances of which have already appeared in the literature as another application we construct stochastic integrals 0 t h s d x s y s associated with certain continuous time martingales x t t 0 and y t t 0 the process x t y t t 0 is shown to be a good integrator although it is not necessarily a semimartingale or even adapted to any convenient filtration

singular integrals with mixed homogeneity in triebel lizorkin spaces abstract in this paper we study the singular integral f x p v r n h y y y f x y d y in triebel lizorkin spaces here l log l s n 1 n 2 h is a measurable locally integrable function defined on 0 and is a norm which is homogeneous with respect to certain non isotropic dilations for the special case when is the usual euclidean norm we also consider the singular integral above in weighted triebel lizorkin spaces for some appropriate weights

bounds for singular fractional integrals and related fourier integral operators abstract we prove sharp lp lq endpoint bounds for singular fractional integral operators and related fourier integral operators under the nonvanishing rotational curvature hypothesis

endpoint estimates for some maximal operators associated to the circular conical surface abstract for c 0 r d and m 0 we consider the maximal operator given by m m f x t sup r 0 r d f x y t y m 1 r d y r d y it is well known that m m is a l p bounded operator for 1 p also a seeger and t tao proved that m m is of weak type l log log l if m 1 in this paper we consider the case m 1 and prove m 1 maps the standard hardy space h 1 to weak l 1 if d 4

robust stability analysis of linear continuous discrete time systems with output feedback controllers the robust stability of linear systems with output feedback controllers and time varying uncertain parameters is considered the robust stability bounds for time varying uncertain parameters are given using the lyapunov method when there are no uncertain parameters in the input and or output matrices it is shown that the result for continuous time systems is the same as that presented by k m zhou and p p khargonekar 1987 and the result for discrete time systems is better than that of s r kolla 1989 for the same example

improved bounds for linear discrete time systems with structured perturbations a time domain analysis of the stability robustness of linear discrete time systems subject to time varying structured perturbations is considered the lyapunov stability theory is used to obtain bounds on the perturbation such that the systems remain stable it is shown that these bounds are less conservative than the existing ones this is illustrated via two numerical examples

rough bilinear singular integrals abstract we study the rough bilinear singular integral introduced by coifman and meyer 8 t f g x p v r n r n y z 2 n y z y z f x y g x z d y d z when is a function in l q s 2 n 1 with vanishing integral and 2 q when q we obtain boundedness for t from l p 1 r n l p 2 r n to l p r n when 1 p 1 p 2 and 1 p 1 p 1 1 p 2 for q 2 we obtain that t is bounded from l 2 r n l 2 r n to l 1 r n for q between 2 and infinity we obtain the analogous boundedness on a set of indices around the point 1 2 1 2 1 to obtain our results we introduce a new bilinear technique based on tensor type wavelet decompositions

boundedness of rough oscillatory singular integral on triebel lizorkin spaces we obtain appropriate sharp bounds on triebel lizorkin spaces for rough oscillatory integrals with polynomial phase by using these bounds and using an extrapolation argument we obtain some new and previously known results for oscillatory integrals under very weak size conditions on the kernel functions

robust c controllability and or c observability for uncertain descriptor systems with interval perturbations in all matrices for descriptor systems of the form ex spl dot t ax t bu t y t cx t existing results are mostly for systems with uncertainties in the a matrix only the case where the e matrix is perturbed renders its robust analysis quite involved and has seldom been touched by researchers this paper will show that if e a b and g are all interval matrices the robust controllability and or observability problems can be solved in terms of the structured singular value p of certain fixed matrices necessary and sufficient conditions are given using the structured singular value spl mu by changing the problem into a robust nonsingularity problem for a class of uncertain matrices

restricted weak type endpoint estimates for k spherical maximal functions in this paper we use the approximation formula for the fourier transform of the solution set of lattice points on k spheres and methods of bourgain and ionescu to refine the ell p mathbb z d boundedness results for discrete k spherical maximal functions to a restricted weak type result at the endpoint we introduce a density parameter which may be viewed as a discrete version of minkowski dimension used in related works on the continuous analgoue in order to exploit recent progress of wooley and bourgain demeter guth on the vinogradov mean value conjectures via a novel approximation formula for a single average and obtain improved bounds for lacunary discrete k spherical maximal functions when k ge 3

one dimensional phase transition problem modeling striped spin orbit coupled bose einstein condensates abstract we study the behavior of a modica mortola phase transition type problem with a non homogeneous neumann boundary condition according to the parameters of the problem this leads to the existence of either one component occupying most of the domain with an outer boundary layer containing the other component or to many interfaces on a periodic pattern this is related to the striped behavior of a two component bose einstein condensate with spin orbit coupling in one dimension we prove that minimizers of the full gross pitaevskii energy in 1d behave in the thomas fermi limit of strong intra component interaction like those of the simplified modica mortola problem we have studied in the first part

new results on restriction of fourier multipliers we develop an extension of the transference methods introduced by r coifman and g weiss and apply it to study the problem of the restriction of fourier multipliers between rearrangement invariant spaces obtaining natural extensions of the classical de leeuw s result and its further extension to maximal fourier multipliers due to c kenig and p tomas

maximal singular integral operators along surfaces abstract let b y be a bounded radial function and y 1 y 2 y m y where each j y j 1 m is a real valued radial function for x y r n and x r m we define the maximal singular integral along the surface y y by t f x x sup e 0 y e f x y x y b y y n y dy suppose that is an h1 function on the sphere sn 1 satisfying sn 1 x d x 0 we prove that t is bounded on lp r n m 1 m g x 1 x sup k z 2 k 2 k 1 2 k g x 1 t x t dt is bounded on lp r m 1 for all p 1 the result is an extension and improvement of the main theorem in s lu y pan and d yang rough singular integrals associated to surfaces of revolution proc amer math soc 129 2001 2931 2940

singular integral operators associated to curves with rational components we prove l p r n 1 0 where rj t p j t q j t j 1 2 n are rational functions our bounds depend only on the degrees of the polynomials pj qj and in particular they do not depend on the coefficients of these polynomials

weak type 1 1 bounds for rough operators ii in this paper we consider four operators arising in harmonic analysis in r n 1 they share one feature each is known to be bounded on lp for all 1 p o but for each it has been an open question whether a weak type 1 1 bound also holds in two cases we show that the weak 1 1 bound does hold and for the others we establish weaker estimates which are still sharper than the lp boundedness although the four operators are quite distinct they all involve convolution kernels which are related to the singular integrals of calderon and zygmund but which lack the smoothness required for the usual analysis in each case this defect is mitigated by the presence of some form of curvature consider the bochner riesz means

singular maximal functions and radon transforms near l 1 we show that some singular maximal functions and singular radon transforms satisfy a weak type l log log l inequality examples include the maximal function and hilbert transform associated to averages along a parabola the weak type inequality yields pointwise convergence results for functions which are locally in l log log l

estimates for singular integrals on homogeneous groups we consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups we prove certain estimates for the operators that imply lp boundedness of them by an extrapolation argument under a sharp condition for the kernels also we prove some weighted lp inequalities for the operators

singular integrals with rough kernels along real analytic submanifolds in r n l p mapping properties will be established in this paper for singular radon transforms with rough kernels defined by translated of a real analytic submanifold in r n

design of robust optimal output feedback controllers for linear uncertain systems using lmi based approach and genetic algorithm this paper considers the robust optimal design problems of output feedback controllers for linear systems with both time varying elemental structured and norm bounded unstructured parameter uncertainties two new sufficient conditions are proposed in terms of linear matrix inequalities lmis for ensuring that the linear output feedback systems with both time varying elemental and norm bounded parameter uncertainties are asymptotically stable where the mixed quadratically coupled parameter uncertainties are directly considered in the problem formulation a numerical example is given to show that the presented sufficient conditions are less conservative than existing ones reported recently then by integrating the hybrid taguchi genetic algorithm htga and the proposed lmi based sufficient conditions a new integrative approach is presented to find the output feedback controllers of the linear systems with both time varying elemental and norm bounded parameter uncertainties such that the control objective of minimizing a quadratic integral performance criterion subject to the stability robustness constraint is achieved a design example of the robust optimal output feedback controller for the afti f 16 aircraft control system with the time varying elemental parameter uncertainties is given to demonstrate the applicability of the proposed new integrative approach

sharp bounds for the commutators with variable kernels of fractional differentiations and bmo sobolev spaces abstract for 0 1 and b i bmo we introduce a new class of commutators with fractional differentiations and variable kernels which is defined by b t f x r n x x y x y n b x b y f y d y in this paper we give the sharp l 2 norm inequalities for the rough operators b t with x z l r n l q s n 1 q 2 n 1 n satisfying the mean zero value condition in its second variable in the sense that the exponent q 2 n 1 n is optimal if strengthen the smoothness of x z in its second variable we prove weight norm inequalities for these operators our results recover a previous result of murray and extend a previous result of calderon

sharp lorentz space estimates for rough operators we demonstrate the h 1 l 1 2 or l p l p 2 mapping properties of several rough operators in all cases these estimates are sharp in the sense that the lorentz exponent 2 cannot be replaced by any lower number