Abstract and Applied Analysis
Volume 2013 (2013), Article ID 473916, 11 pages
http://dx.doi.org/10.1155/2013/473916
Research Article

Product and Commutativity of th-Order Slant Toeplitz Operators

Chaomei Liu1 and Yufeng Lu2

1School of Science, Dalian Jiaotong University, Dalian 116028, China
2School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received 9 November 2012; Revised 12 March 2013; Accepted 14 March 2013

Academic Editor: Miroslaw Lachowicz

Copyright © 2013 Chaomei Liu 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

The commutativity of th-order slant Toeplitz operators with harmonic polynomial symbols, analytic symbols, and coanalytic symbols is discussed. We show that, on the Lebesgue space and Bergman space, necessary and sufficient conditions for the commutativity of th-order slant Toeplitz operators are that their symbol functions are linearly dependent. Also, we study the product of two th-order slant Toeplitz operators and give some necessary and sufficient conditions.