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

LU Mei-lin, LI De-sheng, GUAN Hong-yan

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

Chinese Quarterly Journal of Mathematics >

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

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

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

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.

Received date: 2014-11-27

Online published: 2020-11-24

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Abstract

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

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