On norms of composition operators on weighted hardy spaces

Amenah Essa Shammaky,Sumitra Dalal

doi:10.24297/jam.v14i1.6717

Abstract

The computation of composition operator on Hardy spaces is very hard. In this paper we propose a norm of a bounded composition operator on weighted Hardy spaces H2(b) induced by a disc automorphism by embedding the classical Hardy space . The estimate obtained is accurate in the sense that it provides the exact norm for particular instances of the sequence b. As an application of our results, an estimate for the norm of any bounded composition operator on H2(b) is obtained.

Highlights

Let D denote the open unit disc of the complex plane
1 lim sup n n 1, where the f norm is proposed from the following inner product is in
Z r 1 rz a hyperbolic disc automorphism so that C r is bounded on H 2

Summary

INTRODUCTION

Let D denote the open unit disc of the complex plane. For each sequence of positive numbers n , the weighted Hardy space H 2 consists of analytic functions norm. 1 lim sup n n 1, where the f norm is proposed from the following inner product is in. Observe that particular instances of the sequence n yield well known Hilbert spaces of analytic functions. . If n n 1 2 the norm obtained is equivalent to the one in the Dirichlet space D or if n. If n 1 q for a real number q , the spaces H 2 are known as weighted Dirichlet spaces or S spaces (see [8,10,11,19] , few to mention). For related questions concerning the norm of composition operators

Norm of composition operators on H 2

Rew 1 z belong to n Re w n 1 Re w z n

An application