Chinese Quarterly Journal of Mathematics ›› 2015, Vol. 30 ›› Issue (1): 47-54.doi: 10.13371/j.cnki.chin.q.j.m.2015.01.006

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

  

  1. 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.

Abstract: In this paper, we analyze a class of bounded radial operators on the weighted Bergman space A2α(Bn, d Vα), 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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