p-进中心函数空间及奇异积分算子

引入了几类p-中心函数空间,包括p进A~q和B~q空间、p进λ-中心BMO空间以及p-进中心Morrey空间,得到了p-进A~q空间与B~q空间的对偶性、p-进λ-中心BMO空间和中心Morrey空间的特征,研究了这些空间与加权p-进Lebesgue空间之间的关系.另外,还建立了一类奇异积分算子在p-进中心Morrey空间中的有界性,更进一步,得到了这类算子交换子在p-进中心Morrey空间中的λ-中心BMO估计.     

The Ahlfors–Beurling transform on Morrey spaces with variable exponents

We establish the vector-valued inequalities of the Ahlfors–Beurling operator on Morrey spaces with variable exponents. As consequences of these inequalities, we have the boundedness of the Ahlfors–Beurling transform on Lebesgue spaces with variable exponents and Morrey spaces. The results obtained in this paper are new in the case of Morrey spaces.     

On the coincidence of certain approaches to smoothness spaces related to Morrey spaces

In this paper, we compare the recent approach of Hans Triebel to introduce smoothness spaces related to Morrey‐Campanato spaces with Besov type and Triebel‐Lizorkin type spaces. These two scales have been introduced some years ago and represent a further variant to measure smoothness by using Morrey spaces.     

Weak Morrey spaces with applications

The main object of this investigation is to study weak Morrey spaces. Block spaces, which are preduals of weak Morrey spaces, are characterized. Besides, the Fatou property of block spaces is proved. Finally, as an application, we study the boundedness of singular integral operators in weak Morrey spaces.     

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.     

分数次积分算子在Vilenkin群Morrey空间上的有界性质

引入了Vilenkin群上弱Morrey空间的概念,得到了分数次积分算子在Vilenkin群Morrey空间上的有界性质,特别地,我们给出了在端点处的弱型估计.     

带振荡核奇异积分算子交换子在加权Morrey空间中的有界性质

本文研究Morrey空间中的交换子有界性的问题.利用John-Nirenberg不等式等工具建立带振荡核的奇异积分算子与BMO函数生成交换子在加权Morrey空间中的加权估计.     

Weighted Estimates of Variable Kernel Fractional Integral and Its Commutators on Vanishing Generalized Morrey Spaces with Variable Exponent

In this paper, the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent generalized weighted Morrey spaces and the variable exponent vanishing generalized weighted Morrey spaces. And the corresponding commutators generated by BMO function are also considered.     

Decomposition for Morrey type Besov–Triebel spaces

In this paper, the author establishes the decomposition of Morrey type Besov–Triebel spaces in terms of atoms and molecules concentrated on dyadic cubes, which have the same smoothness and cancellation properties as those of the classical Besov–Triebel spaces. The results extend those of M. Frazier, B. Jawerth for Besov–Triebel spaces and those of A. L. Mazzucato for Besov–Morrey spaces (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

广义Morrey空间上的奇异积分多线性交换子

本文得到了具有混合齐次变量核的奇异积分算子的多线性交换子在广义Morrey空间和加权 Lebesgue空间上的有界性．     

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.     

Besov‐Morrey spaces and Triebel‐Lizorkin‐Morrey spaces on domains

The purpose of this paper is to develop a theory of the Besov‐Morrey spaces and the Triebel‐Lizorkin‐Morrey spaces on domains in R ⁿ. We consider the pointwise multiplier operator, the trace operator, the extension operator and the diffeomorphism operator. Not only to domains in R ⁿ we extend our definition of function spaces to compact oriented Riemannian manifolds. Among the properties above, the result for the trace operator is in particular interesting, which reflects the property of the parameters p, q in the Morrey space ??^p_q (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on domains

In this paper, we consider a non‐smooth atomic decomposition by using a smooth atomic decomposition. Applying the non‐smooth atomic decomposition, a local means characterization and a quarkonical decomposition, we obtain a pointwise multiplier and a trace operator for generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on the whole space. We also develop the theory of those spaces on domains. We consider an extension operator and a trace operator on the upper half space and on compact oriented Riemannian manifolds.     

双线性Fourier乘子算子与Morrey空间

In this paper, by establishing a result concerning the mapping properties for bi(sub)linear operators on Morrey spaces, and the weighted estimates with general weights for the bilinear Fourier multiplier, the author establishes some results concerning the behavior on the product of Morrey spaces for bilinear Fourier multiplier operator with associated multiplierσ satisfying certain Sobolev regularity.     

Doob's inequality,Burkholder-Gundy inequality and martingale transforms on martingale Morrey spaces

We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob's inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob's inequality on martingale block spaces, we obtain the Davis' decompositions for martingale Morrey spaces.     

Besov‐Morrey spaces and Triebel‐Lizorkin‐Morrey spaces for nondoubling measures

We define Morrey type Besov‐Triebel spaces with the underlying measure non‐doubling. After defining the function spaces, we investigate boundedness property of some class of the singular integral operators (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

具有低阶项的散度型椭圆方程的解在Morrey空间上的局部正则性

本文研究了具有低阶项的散度型椭圆方程-(a_(ij)u_(x_i))_(x_j)+b_iu_(x_i)-(d_ju)_(x_j)+cu= (f_j)_(x_j),a．e．x∈Ω的解在Morrey空间上的局部正则性,其中a_(ij)∈VMO∩L~∞(Ω),低阶项系数属于适当的Morrey空间．     

Characterizations of Morrey type Besov and Triebel-Lizorkin spaces with variable exponents

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.