Toeplitz Operators and Division Theorems in Anisotropic Spaces of Holomorphic Functions in the Polydisc

Abstract

This work is an introduction to anisotropic spaces, which have an ω-weight of analytic functions and are generalizations of Lipshitz classes in the polydisc. We prove that these classes form an algebra and are invariant with respect to monomial multiplication. These classes are described in terms of derivatives. It is established that Toeplitz operators are bounded in these (Lipschitz and Djrbashian) spaces. As an application, a theorem about the division by good-inner functions in the mentioned classes is proved.