WEIGHTED HOLOMORPHIC BESOV SPACES AND THEIR BOUNDARY VALUES

We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their boundary functions. Some results about embedding and interpolation are also included.

两类加权空间间的积分算子与离散算子的有界性及算子范数估计

Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.

Boundedness of Maximal Operators and Potential Operators on Carleson Curves in Lebesgue Spaces with Variable Exponent

We prove the boundedness of the maximal operator Mr in the spaces L^p（·）（Г,p） with variable exponent p（t） and power weight p on an arbitrary Carleson curve under the assumption that p（t） satisfies the log-condition on Г. We prove also weighted Sobolev type L^p（·）（Г, p） → L^q（·）（Г, p）-theorem for potential operators on Carleson curves.

Boundedness of Multilinear Singular Integral Operators on Homogeneous Groups

Let G be a homogeneous group. In this paper, the author studies the boundedness of multi-sublinear operators on the product of weighted Lebesgue spaces on G. As its special case, the corresponding result of multilinear Calderon-Zygmund operators can be obtained.

Some Aspects of L_(w_1)~r(G) ∩ L(p,q,w_2dμ)(G)

Let G be a locally compact Abelian group with Haar measure.The authors discuss some basic properties of L_(w_1)~r(G) ∩ L(p,q,w_2dμ)(G) spaces.Then the necessary conditions for compact embeddings of the spaces L_(w_1)~r(R^d)∩L(p,q,w_2dμ)(R^d) are showed.

Sharp weak bounds for n-dimensional fractional Hardy operators

We obtain the operator norms of the n-dimensional fractional Hardy operator Hα（0 〈 α 〈 n） from weighted Lebesgue spaces Lp｜x｜p（R^n） to weighted weak Lebesgue spacesLq,∞｜x｜β（R^n）.

Some Estimates of Bilinear Hausdorff Operators on Stratified Groups

In this paper,we give four kinds of sharp estimates of two variants of bilinear Hausdorff operators on stratified groups,involving weighted Lebesgue spaces,classical Morrey spaces and central Morrey spaces.Meanwhile,some necessary and sufficient conditions of boundness are obtained.

Renormalized Solutions of Nonlinear Parabolic Equations in Weigthed Variable-Exponent Space

This article is devoted to study the existence of renormalized solutions for the nonlinear p （x）-parabolic problem in the Weighted-Variable-Exponent Sobolev spaces, without the sign condition and the coercivity condition.