类奇异积分和交换子在广义Morrey空间上的有界性

The generalized Morrey spaces are introduced under the hypothesis that Rn is endowed with the general parabolic metric , and the boundedness properties are established in generalized Morrey spaces for a class of singular integral operators, which include Calderon-Zygmund singular integrals and their commutators with BMO.     

On Stein's extension operator preserving Sobolev–Morrey spaces

We prove that Stein's extension operator preserves Sobolev–Morrey spaces, that is spaces of functions with weak derivatives in Morrey spaces. The analysis concerns classical and generalized Morrey spaces on bounded and unbounded domains with Lipschitz boundaries in the n‐dimensional Euclidean space.     

A CHARACTERIZATION FOR FRACTIONAL INTEGRALS ON GENERALIZED MORREY SPACES

This paper concerns with the fractional integrals,which are also known as the Riesz potentials.A characterization for the boundedness of the fractional integral operators on generalized Morrey spaces will be presented.Our results can be viewed as a refinement of Nakai’s [7].     

Trudinger's exponential integrability for Riesz potentials of functions in generalized grand Morrey spaces

Our aim in this paper is to discuss Trudinger's exponential integrability for Riesz potentials of functions in generalized grand Morrey spaces. Our result will imply the boundedness of the Riesz potential operator from a grand Morrey space to a Morrey space.     

Spherical limits for Riesz potentials of functions in central generalized Orlicz-Morrey spaces on the unit ball

We introduce central generalized Orlicz–Morrey spaces on the unit ball, and study the weighted behavior of spherical means for Riesz potentials of functions in those spaces. We also treat Orlicz–Morrey–Sobolev functions which are monotone in the punctured unit ball in the sense of Lebesgue.     

A characterization for Adams-type boundedness of the fractional maximal operator on generalized Orlicz–Morrey spaces

In the present paper, we shall give a characterization for weak/strong Adams-type boundedness of the fractional maximal operator on generalized Orlicz–Morrey spaces.     

Remarks on the regularity criteria for generalized MHD equations

We study the Cauchy problem for the generalized MHD equations, and prove some regularity criteria involving the integrability of ∇u in the Morrey, multiplier spaces.     

一些算子的交换子在广义Morrey空间上的紧性

本文主要研究分数次积分算子、Marcinkiewicz积分、带光滑核的pseudo-differential算子的交换子在广义Morrey空间M_p，ω（Rⁿ）上的紧性.注意它们的处理方法分别不同.     

Characterization of the boundedness of generalized fractional integral and maximal operators on Orlicz–Morrey and weak Orlicz–Morrey spaces

We give necessary and sufficient conditions for the boundedness of generalized fractional integral and maximal operators on Orlicz–Morrey and weak Orlicz–Morrey spaces. To do this, we prove the weak–weak type modular inequality of the Hardy–Littlewood maximal operator with respect to the Young function. Orlicz–Morrey spaces contain $L^p$ spaces ($1\le p\le \infty$), Orlicz spaces, and generalized Morrey spaces as special cases. Hence, we get necessary and sufficient conditions on these function spaces as corollaries.     

Sparse non-smooth atomic decomposition of Morrey spaces

Recently, a non-smooth atomic decomposition in Morrey spaces was obtained by the author, Iida and Tanaka. This note refines the above existing result using the notion of sparse families. As an application, we prove the equivalence between fractional integral operators and fractional maximal operators under the Morrey norm.     

Parabolic equations with VMO coefficients in generalized Morrey spaces

In this paper, the authors establish the regularity in generalized Morrey spaces of solutions to parabolic equations with VMO coefficients by means of the theory of singular integrals and linear commutators.     

Bochner-Riesz算子在加权Morrey空间上的一些估计

要本文将得到Bochner-Riesz算子T_R~((n-1)/2)在加权Morrey空间L~(p,k)(w)上的一些强型和弱型估计,1≤P<∞且0相似文献   

Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces

We establish the boundedness and weak boundedness of the maximal operator and generalized fractional integral operators on generalized Morrey spaces over metric measure spaces without the assumption of the growth condition on μ. The results are generalization and improvement of some known results. We also give the vector‐valued boundedness. Moreover we prove the independence of the choice of the parameter in the definition of generalized Morrey spaces by using the geometrically doubling condition in the sense of Hytönen.     

Regularity of the Solution to the Dirichlet Problem in Morrey Spaces

The aim of this paper is to study Morrey regularity of the solution to the Dirichlet problem for second order elliptic equation of the form Lu = -(a_{ij}u_x_i + b_j_u)_x_j + du = e + (f_j)x_j in a bounded open subset of Rn(n ≥ 3), where b_j , d, e, f_j are assumed to be in some Morrey spaces.     

Characterization of multiplier spaces by wavelets and logarithmic Morrey spaces

In this paper, we consider multipliers from Sobolev spaces to Lebesgue spaces. We establish some wavelet characterization of multiplier spaces without using capacity. Further, we give a sharp logarithmic Morrey space condition for multipliers which lessens Fefferman’s Morrey space condition to the logarithm level and generalizes Lemarié’s counter-example to non-integer cases and expresses his results in a more precise way.     

On some hyperbolic type equations and weighted anisotropic Hardy operators

We introduce a version of weighted anisotropic Morrey spaces and anisotropic Hardy operators. We find conditions for boundedness of these operators in such spaces. We also reveal the role of these operators in solving some classes of degenerate hyperbolic partial differential equations. Copyright © 2016 John Wiley & Sons, Ltd.     

Weak Morrey spaces and strong solutions to the Navier-Stokes equations

We consider the Cauchy problem of Navier-Stokes equations in weak Morrey spaces. We first define a class of weak Morrey type spaces Mp*,λ(Rn) on the basis of Lorentz space Lp,∞ = Lp*(Rn)(in particular, Mp*,0(Rn) = Lp,∞, if p ＞ 1), and study some fundamental properties of them; Second,bounded linear operators on weak Morrey spaces, and establish the bilinear estimate in weak Morrey spaces. Finally, by means of Kato's method and the contraction mapping principle, we prove that the Cauchy problem of Navier-Stokes equations in weak Morrey spaces Mp*,λ(Rn) (1＜p≤n) is time-global well-posed, provided that the initial data are sufficiently small. Moreover, we also obtain the existence and uniqueness of the self-similar solution for Navier-Stokes equations in these spaces, because the weak Morrey space Mp*,n-p(Rn) can admit the singular initial data with a self-similar structure. Hence this paper generalizes Kato's results.     

次线性算子在一类广义Morrey空间上的有界性及其应用

证明了一组次线性算子及其交换子,如具有粗糙核的Calderón-Zygmund算子、Ricci-Stein振荡奇异积分、Marcinkiewicz积分、分数次积分和振荡分数次积分及其交换子,在一类广义Morrey空间上的有界性.作为应用得到了非散度型椭圆方程在上述Morrey空间的内部正则性.     

MULTILINEAR CALDERóN-ZYGMUND OPERATOR ON MORREY TYPE SPACES——In Memory of Professor Yongsheng Sun

In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding results of multilinear Calderon-Zygmund operator can be obtained.     

WEAK TYPE INEQUALITIES FOR FRACTIONAL INTEGRAL OPERATORS ON GENERALIZED NON-HOMOGENEOUS MORREY SPACES

We obtain weak type (1,q) inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces.The proofs use some properties of maximal operators.Our results are closely related to the strong type inequalities in [13,14,15].