Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 353801, 22 pages
doi:10.1155/2009/353801
Research Article

Analytic Classes on Subframe and Expanded Disk and the ℛs Differential Operator in Polydisk

Romi F. Shamoyan1 and Olivera R. Mihić2

1Department of Mathematics, Bryansk University, 241036 Bryansk, Russia
2Faculty of Organizational Sciences, University of Belgrade, Jove Ilića 154, 11000 Belgrade, Serbia

Received 25 November 2008; Revised 17 September 2009; Accepted 28 September 2009

Academic Editor: Narendra Kumar Govil

Copyright © 2009 Romi F. Shamoyan and Olivera R. Mihić. 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 introduce and study new analytic classes on subframe and expanded disk and give complete description of their traces on the unit disk. Sharp embedding theorems and various new estimates concerning differential ℛs operator in polydisk also will be presented. Practically all our results were known or obvious in the unit disk.