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.
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 operator in polydisk also will be presented. Practically all our results were known or obvious in the unit disk.