单位球加权Bergman空间上的Berezin变换与径向算子

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

数学季刊 ›› 2015, Vol. 30 ›› Issue (1): 47-54.doi: 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

Department of Mathematics, Shenyang Normal University

收稿日期:2014-11-27 出版日期:2015-03-30 发布日期:2020-11-24
作者简介: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.

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

Department of Mathematics, Shenyang Normal University

Received:2014-11-27 Online:2015-03-30 Published:2020-11-24
About author: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.

摘要/Abstract

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.

中图分类号:

O177

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.

LU Mei-lin, LI De-sheng, GUAN Hong-yan. The Berezin Transform and Radial Operators on the Weighted Bergman Space of the Unit Ball[J]. Chinese Quarterly Journal of Mathematics, 2015, 30(1): 47-54.

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单位球加权Bergman空间上的Berezin变换与径向算子

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

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