Sobolev's inequality for Riesz potentials of functions in Morrey spaces of integral form

Morrey spaces have become a good tool for the study of existence and regularity of solutions of partial differential equations. Our aim in this paper is to give Sobolev's inequality for Riesz potentials of functions in Morrey spaces (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sobolev embeddings into spaces of Campanato, Morrey, and Hölder type

Necessary and sufficient conditions on a rearrangement-invariant Banach function space X(Q) on a cube Q in , n?2, are given for the corresponding Sobolev space W¹X(Q) to be continuously embedded into (generalized) Campanato, Morrey, or Hölder spaces. The optimal such r.i. spaces X(Q) are found. As a by-product, sharp inclusion relations are proved among Campanato, Morrey, and Hölder type spaces.     

Improved decay rates for solutions to one-dimensional linear and semilinear dissipative wave equations in all space

Better decay estimates to the 1-dimensional Cauchy problem on to the linear equation □u+u_t=0 can be discussed under rather restricted conditions on the initial data. Furthermore, as applications we derive the small data global existence result to the equation □u+u_t=|u|^p−1u, which has the “odd” functions as the initial data. Furthermore, the new method (see R. Ikehata, T. Matsuyama, Sci. Math. Japon. 55 (2002) 33-42) used in the first half will be applied to the problem coming from Ehrenpreis (Sugaku 26 (1974) 168).     

Toeplitz Operator Related to Singular Integral with Non-Smooth Kernel on Weighted Morrey Space

Let T_1 be a singular integral with non-smooth kernel or ± I, let T_2 and T_4 be the linear operators and let T_3= ±I. Denote the Toeplitz type operator by T~b= T_1M~bI_αT_2+T_3I_αM~bT_4,where M~bf=bf, and I_α is the fractional integral operator. In this paper, we investigate the boundedness of the operator T~b on the weighted Morrey space when b belongs to the weighted BMO space.     

Embeddings of weighted Morrey spaces

We consider embedding theorems within the scale of weighted Morrey spaces , where the weight w belongs to the Muckenhoupt class and . This includes, in particular, the classical setting of weighted Lebesgue spaces. We study some typical examples for the weight like , but also deal with quite general assumptions.     

Calderón-Zygmund型算子及其交换子的

该文建立了Calderón-Zygmund型算子及其交换子的sharp极大函数估计. 作为应用, 可以得到这些算子在Lebesgue空间和Morrey型空间上的有界性.     

齐型空间上的广义Morrey空间与广义Campanato空间

将经典的Lebesgue微分理论推广到齐型空间上,在齐型空间上定义了广义Morrey空间与广义Campanato空间,并研究了齐型空间（X,d,μ）上的广义Morrey空间与可积空间等的关系以及广义Campanato空间与广义Morrey空间和Holder空间的关系.     

Hardy-Littlewood最大算子的两个推广

§1IntroductionHardy-Littlewood maximal operator has wide applications in many fields,such asquasiconformal analysis,partial differential equations(PDEs)and harmonic analysis.LetΩbe an open subset of Rn,the Hardy-Littlewood maximal operator is defined on Ll1oc(Ω)by the ruleMh(x)=MΩh(x)=sup∫-B(x,t)h(y)dy:0相似文献