Products of weighted composition and differentiation operators into weighted Zygmund and Bloch spaces

We characterize boundedness and compactness of products of differentiation operators and weighted composition operators between weighted Banach spaces of analytic functions and weighted Zygmund spaces or weighted Bloch spaces with general weights.     

Interpolation for martingale Hardy spaces over weighted measure spaces

Several interpolation theorems on martingale Hardy spaces over weighted measure spaces are given. Our proofs are based on the atomic decomposition of martingale Hardy spaces over weighted measure spaces. As applications of interpolation theorems, some inequalities of martingale transform operator are obtained.     

WAVELET CHARACTERIZATION OF WEIGHTED TRIEBEL－LIZORKIN SPACES

In this paper we use wavelets to characterize weighted Triebel-Lizorkin spaces,Our weights belong to the Muckenhoupt class Aq and our weighted Triebel-Lizorkin spaces are weighted atomic Triebel-Lizorkin spaces.     

Wavelet characterization of weighted Triebel-Lizorkin spaces

In this paper we use wavelets to characterize weighted Triebel-Lizorkin spaces. Our weights belong to the Muckenhoupt class Aq and our weighted Triebel-Lizorkin spaces are weighted atomic Triebel-Lizorkin spaces.     

Norm-attaining weighted composition operators on weighted Banach spaces of analytic functions

We investigate weighted composition operators that attain their norm on weighted Banach spaces of holomorphic functions on the unit disc of type H ^∞. Applications for composition operators on weighted Bloch spaces are given.     

Sharpness of some properties of weighted modulation spaces

We obtain some optimal properties on weighted modulation spaces. We find the necessary and sufficient conditions for product inequalities, convolution inequalities and embedding on weighted modulation spaces. Especially, we establish the analogue of the sharp Sobolev embedding theorem on weighted modulation spaces.     

Geodesics on weighted projective spaces

We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases one can “hear” the weights of a weighted projective space.     

Boundedness of generalized fractional integrals in weighted Herz-type spaces

In this paper, the authors investigate the boundedness of the generalized fractional integrals of Pérez on the weighted Herz spaces, the weighted weak Herz spaces and the weighted Herz-type Hardy spaces for general weights.     

Boundedness of generalized fractional integrals in weighted Herz-type spaces

In this paper, the authors investigate the boundedness of the generalized fractional integrals of Pérez on the weighted Herz spaces, the weighted weak Herz spaces and the weighted Herz-type Hardy spaces for general weights. This project was partially supported by the SEDF and the NNSF of China.     

Interpolation theorem on Lorentz spaces over weighted measure spaces

In 1997 Ferreyra proved that it is impossible to extend the Stein-Weiss theorem in the context of Lorentz spaces. In this paper we obtain an interpolation theorem on Lorentz spaces over weighted measure spaces.

     

Carleson-Sobolev measures for weighted Bloch spaces

Carleson-Sobolev measures for weighted Bloch spaces on the unit ball of Cn are described. The classical Carleson measures for growth spaces on special circular domains are characterized.     

Composition operators on weighted Dirichlet spaces

We characterize bounded and compact composition operators on weighted Dirichlet spaces. The method involves integral averages of the determining function for the operator, and the connection between composition operators on Dirichlet spaces and Toeplitz operators on Bergman spaces. We also present several examples and counter-examples that point out the borderlines of the result and its connections to other themes.

     

THE BOUNDEDNESS OF MULTILINEAR COMMUTATORS ON WEIGHTED SPACES AND HERZ-TYPE SPACES

The boundedness of maximal multilinear commutator on certain weighted spaces is obtained. The boundedness of mulitilinear commutators of singular integrals with Calderon-Zygmund kernel on Herz-type spaces is also considered.     

Characterizations of weighted Besov and Triebel-Lizorkin spaces via temperatures

Hardy-Littlewood type characterizations (via temperatures on a half-space) of weighted Besov and Triebel-Lizorkin spaces studied recently by the author are given. In the proof of the sufficient parts of the results, a “sub-mean-value property” of temperatures is used in an elegant way to get control of certain terms by the Hardy maximal function or its vector-valued version. As a byproduct of the results, another characterization of weighted Hardy spaces as well as characterizations of the Gauss-Weierstrass integrals on a strip domain of distributions in the above weighted spaces is obtained also.     

广义分数次积分算子在加权Herz型Hardy空间的有界性

利用加权Herz型Hardy空间的原子分解理论,讨论了广义分数次积分算子Tl从加权Lp空间到加权Lq空间,以及从加权Herz型Hardy空间到加权Herz空间的有界性问题.将已有的分数次积分算子的结论推广到广义分数次积分算子的情形.     

The finite Hilbert transform and weighted Sobolev spaces

The boundedness of the finite Hilbert transform operator on certain weighted L_p spaces is well known. We extend this result to give the boundedness of that operator on certain weighted Sobolev spaces. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the spectrum of difference and differential operators in weighted spaces

We describe the spectrum of weighted shift operators in weighted Banach spaces of two-sided vector sequences. Applications to differential operators in weighted function spaces are given.     

Toeplitz operators on weighted Hardy and Besov spaces

We obtain estimates of the norm of Toeplitz operators on weighted Hardy and Besov spaces. As an application we give characterizations of some spaces of pointwise multipliers.     

Atomic decomposition for weighted Besov and Triebel‐Lizorkin spaces

Rychkov defined weighted Besov spaces and weighted Triebel‐Lizorkin spaces coming with a weight in the class $A_p^{\rm loc}$, which is even wider than the class A_p due to Muckenhoupt. In the present paper we are concerned with the atomic decomposition of these spaces. As an application, we obtain some key theorems in the theory of function spaces. Finally we conclude this paper with some helpful examples showing the difference between weighted spaces and unweighted spaces.     

Cantor sets and cyclicity in weighted Dirichlet spaces

We treat the problem of characterizing the cyclic vectors in the weighted Dirichlet spaces, extending some of our earlier results in the classical Dirichlet space. The absence of a Carleson-type formula for weighted Dirichlet integrals necessitates the introduction of new techniques.