Abstract and Applied Analysis
Volume 2012 (2012), Article ID 958201, 21 pages
http://dx.doi.org/10.1155/2012/958201
Research Article

Toeplitz Operators on the Dirichlet Space of

HongZhao Lin1,2 and YuFeng Lu1

1School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, China
2College of Computer and Information, Fujian Agriculture and Forestry University, Fujian 350002, China

Received 13 August 2012; Accepted 10 October 2012

Academic Editor: Alberto Fiorenza

Copyright © 2012 HongZhao Lin and YuFeng Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the algebraic properties of Toeplitz operators on the Dirichlet space of the unit ball . We characterize pluriharmonic symbol for which the corresponding Toeplitz operator is normal or isometric. We also obtain descriptions of conjugate holomorphic symbols of commuting Toeplitz operators. Finally, the commuting problem of Toeplitz operators whose symbols are of the form is studied.