Composition operators on Hardy Spaces

Let ϕ be a self-map of the unit disk and let C ϕ denote the composition operator with symbol ϕ. We also consider the special case when ϕ and ψ are

The germs at 0 of these new fibre-integrals, to which we add the function 1, have the structure of a C{s, s}-module; this module tensored by C[[s, s]] gives a C[[s, s]]-module

A special class of Hardy type operators related to fiber algebras is used in Section 2 to obtain a version of the Iversen theorem on cluster sets of bounded analytic functions..

(For the case q = 1, this proof was also given in [11].) In fact, it shows that certain cases of Theorem (3.1) are equivalent to Doob’s results.. We end the section by deriving the

COPYRIGHT c by Publishing Department Rzesz´ ow University of Technology P.O... Then according to a classical result of Kuniyeda, Montel and Toya

This paper completes the results of paper [11] in which regu- larity of solutions to equations with elliptic corner operators (i.e. n-dimensional Fuchsian operators) is studied in

Since we have here a concrete normal extension N (namely, multiplication by ψ on some L 2 -space of automorphic vector-valued functions on ∂D), we may directly establish in this

Theorem 3.1. Assume that P is a nonexpansive locally and globally concentrating Markov operator. The Cauchy condition can be expressed in the following way: there is N ∈ N such