调和Dirichlet空间上Toeplitz算子与小Hankel算子的交换性

COMMUTATIVITY OF TOEPLITZ OPERATOR AND SMALL HANKEL OPERATOR ON HARMONIC DIRICHLET SPACE

本文研究了调和Dirichlet空间上调和符号的Toeplitz算子与小Hankel算子交换性的问题.利用算子矩阵表示的方法,获得了调和Dirichlet空间上调和符号的Toeplitz算子与小Hankel算子交换的充要条件,将Dirichlet空间上的相应结果推广到了调和Dirichlet空间上.

In this paper, we study the commutativity of Toeplitz operator and small Hankel operator on harmonic Dirichlet space. By the matrix representation of Toeplitz operator and small Hankel operator, we obtain the necessity and sufficient condition for Toeplitz operator and small Hankel operator on harmonic Dirichlet space to be commutativity, which extends the corresponding results on Dirichlet space.