Abstract and Applied Analysis
Volume 2010 (2010), Article ID 603968, 7 pages
doi:10.1155/2010/603968
Research Article

Carleson Measure in Bergman-Orlicz Space of Polydisc

An-Jian Xu1,2 and Zou Yang3

1Department of Mathematics, Zhejiang University, Hangzhou 310027, China
2Institute of Applied Mathematics, Chongqing University of Post and Telecommunication, Chongqing 400065, China
3Department of Mathematics, Chongqing Education College, Chongqing 400067, China

Received 30 June 2010; Revised 26 August 2010; Accepted 2 September 2010

Academic Editor: Dumitru Baleanu

Copyright © 2010 An-Jian Xu and Zou Yang. 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

Let μ be a finite, positive measure on 𝔻n, the polydisc in ℂn, and let σn be 2n-dimensional Lebesgue volume measure on 𝔻n. For an Orlicz function φ, a necessary and sufficient condition on μ is given in order that the identity map J:Laφ(𝔻n,σn)→Lφ(𝔻n,μ) is bounded.