Algebraic properties of Toeplitz and small Hankel operators on the harmonic Bergman space

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• 作者：Hong Yan Guan (1) (2)
  Yu Feng Lu (1)
  
• 关键词：Toeplitz operator ; small Hankel operator ; quasihomogeneous symbols ; harmonic Bergman space ; Mellin transform ; 47B35
• 刊名：Acta Mathematica Sinica
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：30
• 期：8
• 页码：1395-1406
• 全文大小：228 KB
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• 作者单位：Hong Yan Guan (1) (2)
  Yu Feng Lu (1)
  
  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, P. R. China
  2. School of Mathematics and Systems Science, Shenyang Normal University, Shenyang, 110034, P. R. China
  
• ISSN：1439-7617

文摘

In this paper, we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C. We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator. Meanwhile, we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.