加权Bergman空间上Berezin变换和Hankel算子乘积

卢玉峰;杨君;

数学学报 ›› 2009 ›› Issue (04) : 43-54.

数学学报 ›› 2009 ›› Issue (04) : 43-54. DOI: 10.12386/A2009sxxb0083
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加权Bergman空间上Berezin变换和Hankel算子乘积

    卢玉峰;杨君;
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Berezin Transform and Hankel Products on the Weighted Bergman Space A_α~2

    Yu Feng LU Jun YANG Department of Applied Mathematics,Dalian University of Technology, Dalian 116024,P.R.China
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摘要

首先证明了加权Bergman空间A_α~2上不变拉普拉斯和Berezin变换是可交换的.其次对稠定义在A_α~2上以平方可积函数f和g为符号的Hankel算子乘积H_fH_g~*的有界性给出了一个充分条件.最后完全描述了A_α~2上Hankel算子乘积何时是紧的并且对混合Haplitz乘积也得到了相似结论.

Abstract

First,we prove the fact that the invariant Laplacian commutes with the Berezin transform on the weighted Bergman space A_α~2.Secondly,we consider the question for which square integral functions f and g on A_α~2 the densely defined products H_fH_g~* are bounded and give a sufficient condition.Furthermore,We will completely describe when Hankel products on A_α~2 are compact.We also obtain similar results for the mixed Haplitz products H_gT■ and T_fH_g~*,where f and g are square integrable on the unit disk and f is analytic.

关键词

加权Bergman空间 / Berezin变换 / Toeplitz算子

Key words

Toeplitz operatorkernel / weighted Bergman space / Berezin transform

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卢玉峰;杨君;. 加权Bergman空间上Berezin变换和Hankel算子乘积. 数学学报, 2009(04): 43-54 https://doi.org/10.12386/A2009sxxb0083
Yu Feng LU Jun YANG Department of Applied Mathematics,Dalian University of Technology, Dalian 116024,P.R.China. Berezin Transform and Hankel Products on the Weighted Bergman Space A_α~2. Acta Mathematica Sinica, Chinese Series, 2009(04): 43-54 https://doi.org/10.12386/A2009sxxb0083

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