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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 210596, 15 pages
http://dx.doi.org/10.1155/2011/210596
Research Article

Toeplitz Operators on the Weighted Pluriharmonic Bergman Space with Radial Symbols

1School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
2College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028000, China

Received 3 June 2011; Revised 20 July 2011; Accepted 21 July 2011

Academic Editor: Natig Atakishiyev

Copyright Š 2011 Zhi Ling Sun and Yu Feng 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 construct an operator 𝑅 whose restriction onto weighted pluriharmonic Bergman Space 𝑏2𝜇(𝔹𝑛) is an isometric isomorphism between 𝑏2𝜇(𝔹𝑛) and 𝑙#2. Furthermore, using the operator 𝑅 we prove that each Toeplitz operator 𝑇𝑎 with radial symbols is unitary to the multication operator 𝛾a,𝜇I. Meanwhile, the Wick function of a Toeplitz operator with radial symbol gives complete information about the operator, providing its spectral decomposition.