arXiv subjects

Haihua Wei

Publications and source records attributed to Haihua Wei.

3 recordsLinked to original sources

arXiv2026

A Bloch type space associated with λ-analytic functions

For $λ\ge0$, the so-called $λ$-analytic functions are defined in terms of the (complex) Dunkl operators $D_{z}$ and $D_{\bar{z}}$. In the paper we introduce a Bloch type space on the disk ${\mathbb D}$ associated with $λ$-analytic functions, called the $λ$-Bloch space and denoted by ${\mathfrak{B}}_λ({\mathbb D})$. Various properties of the $λ$-Bloch space ${\mathfrak{B}}_λ({\mathbb D})$ are proved. We give a characterization of functions in ${\mathfrak{B}}_λ({\mathbb D})$ by means of the higher-order operators $(D_z\circ z)^n$ for $n\ge2$. A general integral operator is proved to be bounded from $L^{\infty}({\mathbb D})$ onto ${\mathfrak{B}}_λ({\mathbb D})$, and as an application, the dual relation of ${\mathfrak{B}}_λ({\mathbb D})$ and the $λ$-Bergman space ($p=1$) is verified.

math.CV↗

arXiv2023

Some aspects of the Bergman and Hardy spaces associated with a class of generalized analytic functions

For $λ\ge0$, a $C^2$ function $f$ defined on the unit disk ${\mathbb D}$ is said to be $λ$-analytic if $D_{\bar{z}}f=0$, where $D_{\bar{z}}$ is the (complex) Dunkl operator given by $D_{\bar{z}}f=\partial_{\bar{z}}f-λ(f(z)-f(\bar{z}))/(z-\bar{z})$. The aim of the paper is to study several problems on the associated Bergman spaces $A^{p}_λ({\mathbb D})$ and Hardy spaces $H_λ^p({\mathbb D})$ for $p\ge2λ/(2λ+1)$, such as boundedness of the Bergman projection, growth of functions, density, completeness, and the dual spaces of $A^{p}_λ({\mathbb D})$ and $H_λ^p({\mathbb D})$, and characterization and interpolation of $A^{p}_λ({\mathbb D})$.

math.CV↗

arXiv2022

Boundedness of operators on the Bergman spaces associated with a class of generalized analytic functions

The purpose of the paper is to study the operators on the weighted Bergman spaces on the unit disk ${\mathbb{D}}$, denoted by $A^{p}_{λ,w}({\mathbb{D}})$, that are associated with a class of generalized analytic functions, named the $λ$-analytic functions, and with a class of radial weight functions $w$. For $λ\ge0$, a $C^2$ function $f$ on ${\mathbb D}$ is said to be $λ$-analytic if $D_{\bar{z}}f=0$, where $D_{\bar{z}}$ is the (complex) Dunkl operator given by $D_{\bar{z}}f=\partial_{\bar{z}}f-λ(f(z)-f(\bar{z}))/(z-\bar{z})$. It is shown that, for $2λ/(2λ+1)\le p\le1$, the boundedness of an operator from $A^{p}_{λ,w}({\mathbb{D}})$ into a Banach space depends only upon the norm estimate of a single vector-valued $λ$-analytic function. As applications, we obtain a necessary and sufficient conditions of sequence multipliers on the spaces $A^{p}_{λ,w}({\mathbb{D}})$ for general weights $w$, and characterize the dual space of $A^{p}_{λ,w}({\mathbb{D}})$ for the power weight $w=(1-|z|^2)^{α-1}$ with $α>0$, and also give a sufficient condition of Carleson type for boundedness of multiplication operators on $A^{p}_{λ,w}({\mathbb{D}})$.

math.CV↗