Algebraic Properties of Toeplitz and Small Hankel Operators on the Harmonic Bergman Space  

作　　者：Hong Yan GUAN Yu Feng LU 

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology [2]School of Mathematics and Systems Science,Shenyang Normal University

出　　处：《Acta Mathematica Sinica,English Series》2014年第8期1395-1406,共12页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11271059)

摘　　要：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.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.

关 键 词：Toeplitz operator small Hankel operator quasihomogeneous symbols harmonic Bergman space Mellin transform 

分 类 号：O177[理学—数学]