Generalized Morrey spaces and trace operator

The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. The trace property is one of the main focuses of the present paper, which will clarify the role of the parameter of generalized Morrey spaces. The quarkonial decomposition is obtained as an application of the atomic decomposition. In the end, the relation between the function spaces dealt in the present paper and the foregoing researches is discussed.     

Weighted Morrey spaces and a singular integral operator

In this paper, we shall introduce a weighted Morrey space and study the several properties of classical operatorsin harmonic analysis on this space (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Riesz potential operator in continual variable exponents Herz spaces

We find conditions on the variable parameters $p\left(x\right),q\left(t\right)$ and $\alpha \left(t\right)$, defining the Herz space $H^{p(·),q(·),\alpha (·)}\left({\mathbb{R}}^n\right)$, for the validity of Sobolev type theorem for the Riesz potential operator to be bounded within the frameworks of such variable exponents Herz spaces. We deal with a “continual” version of Herz spaces (which coincides with the “discrete” one when q is constant).     

MULTILINEAR CALDERON-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 Calderón-Zygmund operator can be obtained.     

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.     

Some estimates of maximal commutators for Bochner-Riesz operator on Morrey spaces

In this note, the authors show the boundedness of the maximal commutators of Bocher-Riesz operator B ^δ and that of maximal commutator B _δ1* ^b generated by B ^δ and a Lipschitz function b mapping from M _p ^q (R ⁿ ) into BMO space and also maps from M _p ^q (R ⁿ ) into L _(β−n/q).     

一类次线性算子在加权Herz型Hardy空间上的有界性

得到了新Ｃａｌｄｅｒｏｎ－Ｚｙｈｍｕｎｄ算子的Ｈ Ｋ_ｑ~（ａ,ｐ）（ｗ_１;Ｗ_２到Ｋ_ｑ~（ａ,ｐ）（ｗ_１;ｗ_２）有界性和Ｈ Ｋ_ｑ~（ａ,ｐ）（１;ｘ~β）到ＨＫ_ｑ~（ａ,ｐ）（１;ｘ~β）有界性．     

加权Morrey空间上分数次极大算子的双权不等式

Ye与Wang研究了Hardy-Littlewood极算子在加权Morrey空间的双权不等式.该文将Ye与Wang的结果拓展到分数次极大算子,此外也得到了Ap型的充分条件.     

The boundedness of maximal Bochner-Riesz operator and maximal commutator on Morrey type spaces

The boundedness of maximal Bochner-Riesz operator Bδ* and that of maximal commutator Bδb,* generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space are established.     

Strong maximal operator and singular integral operators in weighted Morrey spaces on product domains

We introduce the Morrey spaces on product domains and extend the boundedness of strong maximal operator and singular integral operators on product domains to Morrey spaces.     

Decompositions of Besov–Morrey spaces and Triebel–Lizorkin–Morrey spaces

The aim of this paper is to define the Besov–Morrey spaces and the Triebel– Lizorkin–Morrey spaces and to present a decomposition of functions belonging to these spaces. Our results contain an answer to the conjecture proposed by Mazzucato. The first author is supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists. The second author is supported by Fūjyukai foundation and the 21st century COE program at Graduate School of Mathematical Sciences, the University of Tokyo.     

Q spaces and Morrey spaces

We characterize functions in Morrey space by p-Carleson measures. We then reveal a simple relation between Q space and Morrey space, that is Q space can be viewed as a fractional integration of the Morrey space. Therefore, many results for Morrey space can be translated onto Q space. For example, we show that Q space is a dual space by identifying its predual.     

On Burenkov's extension operator preserving Sobolev–Morrey spaces on Lipschitz domains

We prove that Burenkov's extension operator preserves Sobolev spaces built on general Morrey spaces, including classical Morrey spaces. The analysis concerns bounded and unbounded open sets with Lipschitz boundaries in the n‐dimensional Euclidean space.     

Morrey spaces in harmonic analysis

Through a geometric capacitary analysis based on space dualities, this paper addresses several fundamental aspects of functional analysis and potential theory for the Morrey spaces in harmonic analysis over the Euclidean spaces.     

Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces

We will prove that for 1相似文献   

Multipliers and Herz type spaces

Hrmander condition for boundedness of multiplier operators will be replaced by a weaker condition described by certain weighted or non-weighted Herz spaces. Some results on boundedness of multiplier operators are then established. As direct corollaries of main theorems in this paper, several celebrated results on boundedness of multiplier operators will be improved or deduced.     

Besov spaces and Herz spaces on local fields

The relationship of Besov spaces and Herz spaces on local fields is given. As an application, one multiplier theorem is obtained. And the decompositional characterization of the weighted Besov spaces is established.     

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.     

Commutators and generalized local Morrey spaces

In this paper we study the behavior of Hardy–Littlewood maximal operator and the action of commutators in generalized local Morrey spaces $L{M}_{\{x_0\}}^{p,\phi }({\mathbb{R}}^n)$ and generalized Morrey spaces $M^{p,\phi }({\mathbb{R}}^n)$.