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Journal of Function Spaces and Applications
Volume 5 (2007), Issue 3, Pages 213-230

Bloch spaces of holomorphic functions in the polydisk

Department of Mathematics, Yerevan State University, Alex Manoogian St. 1, 375049, Yerevan, Armenia

Received 1 October 2005

Academic Editor: Jürgan Appell

Copyright © 2007 Hindawi Publishing Corporation. 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.


This work is an introduction to anisotropic spaces of holomorphic functions, which have ω-weight and are generalizations of Bloch spaces to a polydisc. We prove that these classes form an algebra and are invariant with respect to monomial multiplication. Some theorems on projection and diagonal mapping are proved. We establish a description of (Ap(ω))* (or (Hp(ω))* via the Bloch classes for all 0<p1.