boundary trace embedding theorems for variable exponent sobolev spaces we study boundary trace embedding theorems for variable exponent sobolev space w1 p let be an open bounded or unbounded domain in rn satisfying strong local lipschitz condition under the hypotheses that p l 1 infp x supp x n we prove that there is a continuous boundary trace embedding w1 p lq provided q a measurable function on satisfies condition p x q x n 1 p x n p x for x

applications of mixed martingale hardy spaces in fourier analysis abstract in this paper we consider the martingale hardy spaces defined with the help of the mixed l p norm using atomic decomposition and doob s inequality some applications will be shown in fourier analysis such as the uniform boundedness of the partial sums of the walsh fourier series on l p 1 p and the boundedness of the fejer maximal operator from h p to l p 1 2 p as a consequence of the boundedness we get some almost everywhere and norm convergence results

multi symplectic integration of the camassa holm equation the camassa holm equation is rich in geometric structures it is completely integrable bi hamiltonian and it represents geodesics for a certain metric in the group of diffeomorphism here two new multi symplectic formulations for the camassa holm equation are presented and the associated local conservation laws are shown to correspond to certain well known hamiltonian functionals the multi symplectic discretisation of each formulation is exemplified by means of the euler box scheme numerical experiments show that the schemes have good conservative properties and one of them is designed to handle the conservative continuation of peakon antipeakon collisions

variable weak hardy spaces and their applications abstract let p r n 0 be a variable exponent function satisfying the globally log holder continuous condition in this article the authors first introduce the variable weak hardy space on r n wh p r n via the radial grand maximal function and then establish its radial or non tangential maximal function characterizations moreover the authors also obtain various equivalent characterizations of wh p r n respectively by means of atoms molecules the lusin area function the littlewood paley g function or g function as an application the authors establish the boundedness of convolutional type and non convolutional order calderon zygmund operators from h p r n to wh p r n including the critical case when p n n or when p n n where p ess inf x r n p x

a boundedness criterion for generalized calderon zygmund operators in 1965 a p calderon showed the l2 boundedness of the so called first calderon commutator this is one of the first examples of a non convolution operator associated to a kernel which satisfies certain size and smoothness properties comparable to those of the kernel of the hilbert transform these properties together with the l2 boundedness imply the lp boundedness for all p s in 1 oo many operators in analysis such as certain classes of pseudo differential operators and the cauchy integral operator on a curve are associated with kernels having these properties for these operators one of the major questions is if they are bounded on l2 we are going to give necessary and sufficient conditions for such an operator to be bounded on l2 they are essentially that the images of the function 1 under the actions of the operator and its adjoint both lie in bmo in the case of the aforementioned first commutator this can be checked by an integration by parts in the first section we present some basic notions and state the theorem which is proved in sections 2 and 3 in section 4 we show how to recover some classical results in sections 5 and 6 we construct a functional calculus for small perturbations of a and in section 7 we show a connection between the theory of calderon zygmund operators and kato s conjecture it is a pleasure to express our thanks to r r coifman and y meyer for suggesting many elegant simplifications in our proofs and most of the applications we also wish to thank stephen semmes for several pertinent remarks

a modified central discontinuous galerkin method with positivity preserving and well balanced properties for the one dimensional nonlinear shallow water equations abstract in this paper we present a modified central discontinuous galerkin method for solving the nonlinear shallow water equations over variable bottom topography in one dimensional space the proposed method balances exactly the flux gradient and source term in the still water stationary case by adding a correction term to the base scheme and ensures non negativity of the water depth by using special approximations to the bottom together with a positivity preserving limiter meanwhile reduces the computational cost considerably compared with the standard central discontinuous galerkin method by using l 2 projection to obtain an approximation solution numerical tests are presented to illustrate the accuracy and validity of the proposed schemes

arbitrary order exactly divergence free central discontinuous galerkin methods for ideal mhd equations ideal magnetohydrodynamic mhd equations consist of a set of nonlinear hyperbolic conservation laws with a divergence free constraint on the magnetic field neglecting this constraint in the design of computational methods may lead to numerical instability or nonphysical features in solutions in our recent work f li l xu s yakovlev central discontinuous galerkin methods for ideal mhd equations with the exactly divergence free magnetic field journal of computational physics 230 2011 4828 4847 second and third order exactly divergence free central discontinuous galerkin methods were proposed for ideal mhd equations in this paper we further develop such methods with higher order accuracy the novelty here is that the well established h div conforming finite element spaces are used in the constrained transport type framework and the magnetic induction equations are extensively explored in order to extract sufficient information to uniquely reconstruct an exactly divergence free magnetic field the overall algorithm is local and it can be of arbitrary order of accuracy numerical examples are presented to demonstrate the performance of the proposed methods especially when they are fourth order accurate

regularity results for a class of functionals with non standard growth we consider the integral functional under non standard growth assumptions that we call p x type namely we assume that a relevant model case being the functional under sharp assumptions on the continuous function p x 1 we prove regularity of minimizers energies exhibiting this growth appear in several models from mathematical physics

besov spaces with variable smoothness and integrability abstract in this article we introduce besov spaces with variable smoothness and integrability indices we prove independence of the choice of basis functions as well as several other basic properties we also give sobolev type embeddings and show that our scale contains variable order holder zygmund spaces as special cases we provide an alternative characterization of the besov space using approximations by analytic functions

matrix weighted besov spaces nazarov treil and volberg defined matrix ap weights and extended the theory of weighted norm inequalities on l p to the case of vector valued functions we develop some aspects of littlewood paley function space theory in the matrix weight setting in particular we introduce matrix weighted homogeneous besov spaces b q p w and matrix weighted sequence besov spaces b q p w as well as b q p a q where the a q are reducing operators for w under any of three different conditions on the weight w we prove the norm equivalences f b q p w s q q b q p w s q q b q p a q where s q q is the vector valued sequence of transform coefficients of f in the process we note and use an alternate more explicit characterization of the matrix ap class furthermore we introduce a weighted version of almost diagonality and prove that an almost diagonal matrix is bounded on b q p w if w is doubling we also obtain the boundedness of almost diagonal operators on b q p w under any of the three conditions on w this leads to the boundedness of convolution and non convolution type calderon zygmund operators czos on b q p w in particular the hilbert transform we apply these results to wavelets to show that the above norm equivalence holds if the transform coefficients are replaced by the wavelet coefficients finally we construct inhomogeneous matrix weighted besov spaces b q p w and show that results corresponding to those above are true also for the inhomogeneous case

compact accurately boundary adjusting high resolution technique for fluid dynamics a novel high resolution numerical method is presented for one dimensional hyperbolic problems based on the extension of the original upwind leapfrog scheme to quasi linear conservation laws the method is second order accurate on non uniform grids in space and time has a very small dispersion error and computational stencil defined within one space time cell for shock capturing the scheme is equipped with a conservative non linear correction procedure which is directly based on the maximum principle plentiful numerical examples are provided for linear advection quasi linear scalar hyperbolic conservation laws and gas dynamics and comparisons with other computational methods in the literature are discussed

high order central discontinuous galerkin finite element methods for the camassa holm equation in this paper we consider the numerical approximation of the camassa holm equation which supports peakon solutions we develop and test a high order central discontinuous galerkin finite element methods for solving this equation in our numerical approach we first reformulate the camassa holm equation into a conservation law coupled with an elliptic equation then we propose a family of high order numerical methods which discretize the conservation law with central discontinuous galerkin methods and the elliptic equation with continuous finite element methods numerical tests are presented to illustrate the accuracy and robustness of the proposed schemes

convergence of a finite difference scheme for the camassa holm equation we prove that a certain finite difference scheme converges to the weak solution of the cauchy problem on a finite interval with periodic boundary conditions for the camassa holm equation u t u xxt 3uu x 2u xu xx uu xxx 0 with initial data u t 0 u 0 in h 1 0 1 here it is assumed that u 0 u 0 ge0 and in this case the solution is unique globally defined and energy preserving

new real variable characterizations of musielak orlicz hardy spaces abstract let r n 0 0 be such that x is an orlicz function and t is a muckenhoupt a r n weight the musielak orlicz hardy space h r n is defined to be the space of all f s r n such that the grand maximal function f belongs to the musielak orlicz space l r n luong dang ky established its atomic characterization in this paper the authors establish some new real variable characterizations of h r n in terms of the vertical or the non tangential maximal functions or the littlewood paley g function or g function via first establishing a musielak orlicz fefferman stein vector valued inequality moreover the range of in the g function characterization of h r n coincides with the known best results when h r n is the classical hardy space h p r n with p 0 1 or its weighted variant

linear bicharacteristic schemes without dissipation this paper is concerned with developing methods for the propagation of linear waves in several space dimensions the methods are time reversible and hence are free from numerical dissipation they are based on bicharacteristic forms of the governing equations and are made possible by adopting forms of staggered storage that depend on the precise equations under consideration analysis is presented for the equations of acoustics electromagnetics and elastodynamics

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

regularity results for stationary electro rheological fluids we prove regularity results for weak solutions to systems modelling electro rheological fluids in the stationary case as proposed in 27 31 a particular case of the system we consider is

atomic and molecular decompositions of anisotropic triebel lizorkin spaces weighted anisotropic triebel lizorkin spaces are introduced and studied with the use of discrete wavelet transforms this study extends the isotropic methods of dyadic transforms of frazier and jawerth 1985 1989 to non isotropic settings associated with general expansive matrix dilations and a weights in close analogy with the isotropic theory we show that weighted anisotropic triebel lizorkin spaces are characterized by the magnitude of the transforms in appropriate sequence spaces we also introduce non isotropic analogues of the class of almost diagonal operators and we obtain atomic and molecular decompositions of these spaces thus extending isotropic results of frazier and jawerth

a local discontinuous galerkin method for the camassa holm equation in this paper we develop analyze and test a local discontinuous galerkin ldg method for solving the camassa holm equation which contains nonlinear high order derivatives the ldg method has the flexibility for arbitrary h and p adaptivity we prove the l 2 stability for general solutions and give a detailed error estimate for smooth solutions and provide numerical simulation results for different types of solutions of the nonlinear camassa holm equation to illustrate the accuracy and capability of the ldg method

hardy spaces with variable exponents and generalized campanato spaces in the present paper we define hardy spaces with variable exponents on rn by the grand maximal function and then investigate their several properties the present paper will connect harmonic analysis with function spaces with variable exponents we obtain the atomic decomposition and the molecular decomposition with these decomposition proved we investigate the littlewood paley characterization also we specify the dual spaces of hardy spaces with variable exponents they will turn out to be campanato spaces with variable growth conditions the present paper covers local hardy spaces with variable exponents

complex interpolation of besov spaces and triebel lizorkin spaces with variable exponents abstract this paper concerns the complex interpolation of besov spaces and triebel lizorkin spaces with variable exponents

analysis of the parametric models of passive scalar transport used in the lattice boltzmann method abstract the paper is devoted to the analysis of passive scalar transport models used in the lattice boltzmann method the case of the pure advection process without physical diffusion is considered the models proposed by other authors the modifications of these models and new high order finite difference schemes based on the extended runge kutta like formulae are analyzed the attention is focused on the stability analysis analysis of the fictitious numerical effects and on the investigation of the sensitivity of accuracy order to the parameter values the stability analysis is based on the von neumann method the influence of the parameter values on the stability is demonstrated stability conditions are obtained numerical dispersion and diffusion are analyzed test problems with discontinuous and smooth initial conditions are considered the sensitivity of the accuracy order on the parameter values is analyzed

on 2 microlocal spaces with all exponents variable abstract in this paper we study various key properties for 2 microlocal besov and triebel lizorkin spaces with all exponents variable including the lifting property embeddings and fourier multipliers we also clarify and improve some statements recently published

a new non linear two time level central leapfrog scheme in staggered conservation flux variables for fluctuating hydrodynamics equations with gpu implementation abstract for solving landau lifshitz navier stokes fluctuating hydrodynamics equations a two time level modification of the classical central leapfrog scheme with non linear flux correction is developed the new algorithm is simple for implementation and demonstrates high accuracy in satisfying the fluctuation dissipation theorem the numerical results for equilibrium and non equilibrium problems in one dimensional and three dimensional settings are compared with theoretical predictions the results from direct molecular dynamics simulations and also with those of several popular computational schemes in the literature because of simplicity and locality of the computational stencil the new algorithm can be efficiently implemented on the gpu which accelerates the calculation in comparison with a single cpu core computation by a factor of 300

atomic decomposition of besov spaces with variable smoothness and integrability abstract the aim of this paper is twofold first we characterize the besov spaces with variable smoothness and integrability by so called peetre maximal functions secondly we use these results to prove the atomic decomposition for these spaces

harnack s inequality and the strong p laplacian abstract we study solutions of the strong p laplace equation we show that in contrast to p laplace solutions these solutions satisfy the ordinary scale invariant harnack inequality as consequences we derive the strong maximum principle and global integrability of solutions

atomic decomposition of hardy amalgam spaces abstract we define a hardy type space by taking in the maximal characterization of hardy spaces the wiener amalgam norms of the maximal functions instead of the lebesgue norms the functions in this space can then behave differently locally and at infinity we prove that this space contains the classical hardy space and obtain an atomic decomposition

abstract hardy spaces with variable exponents abstract in this paper we introduce the definition of abstract hardy spaces with variable exponents via the atomic decomposition and molecular decomposition we prove the continuity from our variable hardy space h a t o p into l p where p r n 0 1 0 p p 1 moreover we investigate the bilinear theory finally we give an application of the abstract hardy spaces with variable exponents

a discrete transform and decompositions of distribution spaces abstract we study a representation formula of the form q q q for a distribution on r n this formula is obtained by discretizing and localizing a standard littlewood paley decomposition the map taking to the sequence q q with q running over the dyadic cubes in r n is called the transform the functions q and q have a particularly simple form moreover most of the familiar distribution spaces lp spaces 1 r n we also consider pointwise multipliers for the characteristic function of a domain we obtain boundedness results for a general class of domains which properly includes lipschitz domains several interpolation methods are easily analyzed via the sequence spaces for real interpolation we obtain among other things an extension to the case p 0 this in turn gives a new approach to the traditional atomic decomposition of hardy spaces

new efficient high resolution method for nonlinear problems in aeroacoustics this paper is devoted to a new efficient numerical method for aeroacoustic applications the method is second order accurate and it has a very compact numerical stencil it combines traditional merits of finite volume and finite difference approaches such as shock capturing and linear fourier accuracy on coarse grids

non smooth atomic decomposition of 2 microlocal spaces and application to pointwise multipliers abstract we provide non smooth atomic characterizations for 2 microlocal besov and triebel lizorkin spaces with variable integrability b p q w r n and f p q w r n these spaces cover the classical besov and triebel lizorkin spaces as well as spaces of variable smoothness and integrability as an application we state a pointwise multipliers result for these spaces

on various approaches to besov type spaces of variable smoothness abstract the paper is concerned with besov spaces of variable smoothness b p q 0 r n t k in which the norms are defined in terms of convolutions with smooth functions a relation is found between the spaces b p q 0 r n t k and the spaces b p q r l r n t k which were introduced earlier by the author as an application an equivalent description of the trace space of the weighted sobolev space with muckenhoupt weight is given

holder continuity for nonlinear elliptic problem in musielak orlicz sobolev space abstract under appropriate assumptions on the n function the de giorgi process is presented by the tools recently developed in musielak orlicz sobolev space to prove the holder continuity of fully nonlinear elliptic problems as the applications the holder continuity of the minimizers for a class of the energy functionals in musielak orlicz sobolev spaces is proved and furthermore the local holder continuity of the weak solutions for a class of fully nonlinear elliptic equations is provided

on the stability in weak topology of the set of global solutions to the navier stokes equations let x be a suitable function space and let mathcal g subset x be the set of divergence free vector fields generating a global smooth solution to the incompressible homogeneous three dimensional navier stokes equations we prove that a sequence of divergence free vector fields converging in the sense of distributions to an element of mathcal g belongs to mathcal g if n is large enough provided the convergence holds anisotropically in frequency space typically this excludes self similar type convergence anisotropy appears as an important qualitative feature in the analysis of the navier stokes equations it is also shown that initial data which do not belong to mathcal g hence which produce a solution blowing up in finite time cannot have a strong anisotropy in their frequency support

hardy space estimates for limited ranges of muckenhoupt weights abstract in this article we give a full necessary and sufficient set of conditions for a calderon zygmund operator to be bounded on weighted hardy spaces h w p where w is an muckenhoupt weight and 0 p in fact this result is new even when 1 p since it allows for h w p boundedness of an operator when 1 p q and w a q where it is possible that h w p l w p these singular integral results are achieved by proving littlewood paley stein square function type estimates from h w p into l w p for 0 p and a muckenhoupt weight w which are interesting results in their own right new techniques involving a weight invariant spaces are also used to prove the weighted estimates for calderon zygmund operators more precisely we prove the following bmo type weight invariance properties for a fixed s 0 the weighted sobolev bmo spaces i s b m o w coincide for all w a the weighted p type triebel lizorkin spaces f w s 2 coincide for all w a and these two classes of spaces coincide with each other as well all of which have comparable norms up to constants depending on an a p character of the weight w a

calderon zygmund operators on herz type hardy spaces abstract we consider the boundedness of calderon zygmund operators from h k p q r n to h k p q r n where h k p q r n is the hardy space associated with the herz space k p q r n and h k p q r n is the local version of h k p q r n we show calderon s commutator is bounded from h k p q to h k p q

characterizations of morrey type besov and triebel lizorkin spaces with variable exponents abstract in this paper morrey type besov and triebel lizorkin spaces with variable exponents are introduced then equivalent quasi norms of these new spaces in terms of peetre s maximal functions are obtained finally applying those equivalent quasi norms the authors obtain the atomic molecular and wavelet decompositions of these new spaces

multilinear theory of strongly singular calderon zygmund operators and applications abstract the main purpose of this paper is to study the multilinear strongly singular calderon zygmund operator whose kernel is more singular near the diagonal than that of the standard multilinear calderon zygmund operator the sharp maximal estimate for this class of multilinear singular integrals is established and as applications its boundedness on product of weighted lebesgue spaces and product of variable exponent lebesgue spaces is obtained respectively moreover the endpoint estimates of the types l l b m o b m o b m o b m o and l m o l m o l m o are established for the multilinear strongly singular calderon zygmund operator these results improve the corresponding known ones for the standard multilinear calderon zygmund operator furthermore we remove the size condition assumption for the kernel of the multilinear strongly singular calderon zygmund operator which has been imposed in the literature for the case of the standard multilinear calderon zygmund operator to get the sharp maximal estimates see remarks 1 1 1 4 extra care is needed to deal with the mean oscillation over balls with small radius to overcome the stronger singularity in establishing such sharp maximal estimates and endpoint estimates

real interpolation for variable martingale hardy spaces abstract in this paper we consider the real interpolation for variable martingale hardy spaces let 0 q and 0 1 then h p s h s q h p 1 q s where the variable exponent p is a measurable function defined on a probability space the variable exponent does not need any restriction

on trace spaces of 2 microlocal type spaces abstract we study traces in 2 microlocal triebel lizorkin spaces with variable integrability f p q w r n on hyperplanes using atomic decompositions our results cover spaces of variable smoothness and variable integrability and also weighted spaces studied extensively in recent years we also study the trace of besov spaces b p q w r n and triebel lizorkin spaces f p q w r n in a limiting situation i e when w j x 2 j 1 p x for all x r n and j n 0

maximum principles for anisotropic elliptic inequalities we establish some maximum and comparison principles for weak distributional solutions of anisotropic elliptic inequalities in divergence form both in the homogeneous and non homogeneous case the main prototypes we have in mind are inequalities involving the p laplace operator and the generalized mean curvature operator

anisotropic variable hardy lorentz spaces and their real interpolation abstract let p r n 0 be a variable exponent function satisfying the globally log holder continuous condition q 0 and a be a general expansive matrix on r n in this article the authors first introduce the anisotropic variable hardy lorentz space h a p q r n associated with a via the radial grand maximal function and then establish its radial or non tangential maximal function characterizations moreover the authors also obtain characterizations of h a p q r n respectively in terms of the atom and the lusin area function as an application the authors prove that the anisotropic variable hardy lorentz space h a p q r n serves as the intermediate space between the anisotropic variable hardy space h a p r n and the space l r n via the real interpolation this together with a special case of the real interpolation theorem of h kempka and j vybiral on the variable lorentz space further implies the coincidence between h a p q r n and the variable lorentz space l p q r n when ess inf x r n p x 1

a convergent finite difference scheme for the camassa holm equation with general h 1 initial data we suggest a finite dfference scheme for the camassa holm equation that can handle general h 1 initial data the form of the difference scheme is judiciously chosen to ensure that it satisfies a total energy inequality we prove that the difference scheme converges strongly in h 1 towards a dissipative weak solution of the camassa holm equation

embeddings of variable hajlasz sobolev spaces into holder spaces of variable order pointwise estimates in variable exponent sobolev spaces on quasi metric measure spaces are investigated based on such estimates sobolev embeddings into holder spaces with variable order are obtained this extends some known results to the variable exponent setting

variable exponent triebel lizorkin morrey spaces abstract we introduce variable exponent versions of morreyfied triebel lizorkin spaces to that end we prove an important convolution inequality which is a replacement for the hardy littlewood maximal inequality in the fully variable setting using it we obtain characterizations by means of peetre maximal functions and use them to show the independence of the introduced spaces from the admissible system used

function spaces of variable smoothness and integrability abstract in this article we introduce triebel lizorkin spaces with variable smoothness and integrability our new scale covers spaces with variable exponent as well as spaces of variable smoothness that have been studied in recent years vector valued maximal inequalities do not work in the generality which we pursue and an alternate approach is thus developed using it we derive molecular and atomic decomposition results and show that our space is well defined i e independent of the choice of basis functions as in the classical case a unified scale of spaces permits clearer results in cases where smoothness and integrability interact such as sobolev embedding and trace theorems as an application of our decomposition we prove optimal trace theorem in the variable indices case

almost everything you need to know about relatively compact sets in variable lebesgue spaces abstract we study relatively compact sets in variable lebesgue spaces the full characterization of such sets is given in the case of variable lebesgue space on metric measure spaces the paper contains a detailed discussion of relatively compact sets in variable lebesgue space on the euclidean space moreover some applications of the theorems are given

complex interpolation of variable triebel lizorkin spaces abstract we study complex interpolation of variable triebel lizorkin spaces especially we present the complex interpolation of f p q and f p p spaces also some limiting cases are given

overview of differential equations with non standard growth abstract differential equations with non standard growth have been a very active field of investigation in recent years in this survey we present an overview of the field as well as several of the most important results we consider both existence and regularity questions finally we provide a comprehensive list of papers published to date

time asynchronous relative dimension in space method for multi scale problems in fluid dynamics a novel computational method is presented for solving fluid dynamics equations in the multi scale framework when the system size is an important parameter of the governing equations the method tardis is based on a concurrent transformation of the governing equations in space and time and solving the transformed equations on a uniform cartesian grid with the corresponding causality conditions at the grid interfaces for implementation in the framework of tardis the second order cabaret scheme of karabasov and goloviznin 1 is selected for it provides a good combination of numerical accuracy computational efficiency and simplicity of realisation numerical examples are first provided for several isothermal gas dynamics test problems and then for modelling of molecular fluctuations inside a microscopic flow channel and ultrasound wave propagation through a nano scale region of molecular fluctuations

entropy numbers of embeddings of weighted besov spaces iii weights of logarithmic type we determine the exact asymptotic order of the entropy numbers of compact embeddings b s 1 p 1 q 1 mathbb r d w 1 hookrightarrow b s 2 p 2 q 2 mathbb r d w 2 of weighted besov spaces in the case where the ratio of the weights w x w 1 x w 2 x is of logarithmic type this complements the known results for weights of polynomial type the estimates are given in terms of the number 1 p 1 p 1 1 p 2 and the function w x we find an interesting new effect if the growth rate at infinity of w x is below a certain critical bound then the entropy numbers depend only on w x and no longer on the parameters of the two besov spaces all results remain valid for triebel lizorkin spaces as well

compact embeddings in the generalized sobolev space w01 p g and existence of solutions for nonlinear elliptic problems abstract our aim in this paper is to deal with the compact embedding in the generalized sobolev space w 0 1 p g with a variable exponent satisfying the log holder condition as an application we find a nontrivial weak solution of the nonlinear elliptic problem div u x p x 2 u x f x u x in g u x 0 on g which is an extension of fan zhang x fan g h zhang existence of solutions for p x laplacian dirichlet problem nonlinear anal 52 2003 pp 1843 1852 theorem 4 7

some remarks on the hardy littlewood maximal function on variable l p spaces we show that any pointwise multiplier for bmo n generates a function p from the class open image in new window n of those functions for which the hardy littlewood maximal operator is bounded on the variable lp space in particular this gives a positive answer to diening s conjecture saying that there are discontinuous functions which nevertheless belong to open image in new window n

musielak orlicz campanato spaces and applications abstract let r n 0 0 be such that x is an orlicz function and t is a muckenhoupt a r n weight uniformly in t in this article the authors introduce the musielak orlicz campanato space l q s r n as an application the authors prove that some of them is the dual space of the musielak orlicz hardy space h r n which in the case when q 1 and s 0 was obtained by l d ky arxiv 1105 0486 the authors also establish a john nirenberg inequality for functions in l 1 s r n and as an application the authors also obtain several equivalent characterizations of l q s r n which in return further induce the carleson measure characterization of l 1 s r n

atomic and molecular decompositions in variable exponent 2 microlocal spaces and applications abstract in this article we study atomic and molecular decompositions in 2 microlocal besov and triebel lizorkin spaces with variable integrability we show that in most cases the convergence implied in such decompositions holds not only in the distributions sense but also in the function spaces themselves as an application we give a simple proof for the denseness of the schwartz class in such spaces some other properties like sobolev embeddings are also obtained via atomic representations

besov type spaces with variable smoothness and integrability abstract in this article the authors introduce besov type spaces with variable smoothness and integrability the authors then establish their characterizations respectively in terms of transforms in the sense of frazier and jawerth smooth atoms or peetre maximal functions as well as a sobolev type embedding as an application of their atomic characterization the authors obtain a trace theorem of these variable besov type spaces

high order well balanced cdg fe methods for shallow water waves by a green naghdi model in this paper we consider a one dimensional fully nonlinear weakly dispersive green naghdi model for shallow water waves over variable bottom topographies such model describes a large spectrum of shallow water waves and it is thus of great importance to design accurate and robust numerical methods for solving it the governing equations contain mixed spatial and temporal derivatives of the unknowns they also have still water stationary solutions which should be preserved in stable numerical simulations in our numerical approach we first reformulate the green naghdi equations into balance laws coupled with an elliptic equation we then propose a family of high order numerical methods which discretize the balance laws with well balanced central discontinuous galerkin methods and the elliptic part with continuous finite element methods linear dispersion analysis for both the reformulated green naghdi system and versions of the proposed numerical scheme is performed when the bottom topography is flat numerical tests are presented to illustrate the accuracy and stability of the proposed schemes as well as the capability of the green naghdi model to describe a wide range of shallow water wave phenomena

a family of low dispersive and low dissipative explicit schemes for flow and noise computations explicit numerical methods for spatial derivation filtering and time integration are proposed they are developed with the aim of computing flow and noise with high accuracy and fidelity all the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to k x 2 corresponding to four points per wavelength they are shown to be more accurate and also more efficient numerically than most of the standard explicit high order methods for uniform and slowly non uniform grids two problems involving long range sound propagation are resolved to illustrate their respective precisions remarks about their practical applications are then made especially about the connection with the boundary conditions finally their relevance for the simulation of turbulent flows is emphasized

gradient estimates for the p x laplacean system we prove calderon and zygmund type estimates for a class of elliptic problems whose model is the non homogeneous p x laplacean system div jduj p x 2 du div jf j p x 2 f

maximal function characterizations of variable hardy spaces associated with non negative self adjoint operators satisfying gaussian estimates abstract let p r n 0 1 be a variable exponent function satisfying the globally log holder continuous condition and l a non negative self adjoint operator on l 2 r n whose heat kernels satisfying the gaussian upper bound estimates let h l p r n be the variable exponent hardy space defined via the lusin area function associated with the heat kernels e t 2 l t 0 in this article the authors first establish the atomic characterization of h l p r n using this the authors then obtain its non tangential maximal function characterization which when p is a constant in 0 1 coincides with a recent result by l song and l yan 2016 and further induces the radial maximal function characterization of h l p r n under an additional assumption that the heat kernels of l have the holder regularity

new molecular characterizations of anisotropic musielak orlicz hardy spaces and their applications abstract let r n 0 0 be an anisotropic growth function and a a general expansive matrix on r n let h a r n be the anisotropic musielak orlicz hardy space associated with a defined via the non tangential grand maximal function in this article the authors establish a new molecular characterization of h a r n via its known atomic characterizations which positively answer a question mentioned by li et al 2016 34 as an application the authors obtain a criterion on the boundedness of linear operators on h a r n which further implies the boundedness of integral anisotropic calderon zygmund operators on h a r n in addition the boundedness of these operators from h a r n to the musielak orlicz space l r n is also presented

on the boundary blow up solutions of p x laplacian equations with singular coefficient abstract this paper investigates the problem p x u x f x u 0 in u x as d x 0 where p x u div u p x 2 u is called the p x laplacian x is a singular coefficient the existence and nonexistence of boundary blow up solutions are discussed and the singularity of the boundary blow up solution is given

nested iterations for symmetric eigenproblems the evaluation of the leftmost eigenspectrum of large sparse symmetric matrices is of great interest in many physical and engineering applications recently an efficient iterative method called dacg deflation accelerated conjugate gradient based on the conjugate gradient optimization of successive deflated rayleigh quotients was developed in the present paper the authors study the possibility of increasing the efficiency of this scheme by means of a nested iteration ni technique that acts on nested finite element grids and calculates an improved initial guess to be used by the dacg procedure the new ni dacg method is tested on two sample problems of large size which make use of nested regular and irregular finite element grids the results obtained in the calculation of the 40 leftmost eigenpairs for both problems show that the computational efficiency of dacg is increased by a factor of five for the regular mesh and two for the irregular one they also show the limitation of simple low order int