单位球加权Bergman空间上的Berezin变换与径向算子

鲁美麟, 李德生, 关洪岩

doi:10.13371/j.cnki.chin.q.j.m.2015.01.006

数学季刊 >

2015 , Vol. 30 >Issue 1: 47 - 54

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.01.006

单位球加权Bergman空间上的Berezin变换与径向算子

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Department of Mathematics, Shenyang Normal University

LU Mei-lin(1989-), female, native of Shenyang, Liaoning, M.S.D., engages in operator theory of function spaces; LI De-sheng(1963-), male, native of Shenyang, Liaoning, Ph.D., a professor of Shenyang Normal University, engages in operator theory of function spaces; GUAN Hong-yan(1980-), male, native of Shenyang, Liaoning, M.S.D., a lecturer of Shenyang Normal University, engages in operator theory of function spaces.

收稿日期: 2014-11-27

网络出版日期: 2020-11-24

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The Berezin Transform and Radial Operators on the Weighted Bergman Space of the Unit Ball

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Department of Mathematics, Shenyang Normal University

Received date: 2014-11-27

Online published: 2020-11-24

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摘要

In this paper, we analyze a class of bounded radial operators on the weighted Bergman space A²_α(B_n, d V_α), we get that these kinds of operators are diagonal with respect to the standard orthonomal basis. We also investigate the connection between compactness of operators and the boundary behaviour of the corresponding Berezin transform. We further study a special class of radial operators, i.e., Toeplitz operators with a radial L¹ symbol.

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鲁美麟, 李德生, 关洪岩 . 单位球加权Bergman空间上的Berezin变换与径向算子[J]. 数学季刊, 2015 , 30(1) : 47 -54 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.01.006

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