Bloch spaces of holomorphic functions in the polydisk

Abstract

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<p≤1.