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Journal of Function Spaces
Volume 2016 (2016), Article ID 1054768, 9 pages
http://dx.doi.org/10.1155/2016/1054768
Research Article

Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball

School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received 23 October 2015; Accepted 24 December 2015

Academic Editor: Kehe Zhu

Copyright © 2016 Yinyin Hu et al. 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 completely characterize the pluriharmonic symbols for (semi)commuting dual Toeplitz operators on the orthogonal complement of the pluriharmonic Dirichlet space in Sobolev space of the unit ball. We show that, for and pluriharmonic functions, on if and only if and satisfy one of the following conditions: both and are holomorphic; both and are holomorphic; there are constants and , both not being zero, such that is constant.