Norm of an integral operator on some analytic function spaces on the unit disk

Hao Li,Songxiao Li

doi:10.1186/1029-242x-2013-342

Abstract

If f is an analytic function in the unit disc , a class of integral operators is defined as follows: The norm of on some analytic function spaces is computed in this paper. MSC:47B38, 32A35.

Highlights

Let D = {z : |z| < } be the unit disk of a complex plane C
We know that Q = BMOA, the space of all analytic functions of bounded mean oscillation [, ]
Both integral operators have been studied by many authors

Summary

Introduction

For all p > , the space Qp is the same and equal to the Bloch space B, consisting of analytic functions f in D such that f B = f ( ) + sup f (z) – |z| < ∞. For α > , the α-Bloch space, denoted by Bα, is the space of all functions f in D, for which f Bα = f ( ) + sup f (z) – |z| α < ∞. Both integral operators have been studied by many authors. Liu and Xiong discussed the norm of integral operators If and Jf on the Bloch space, Dirichlet space, BMOA space and so on in [ ]. We study the norm of integral operator If. The norm of If on several analytic function spaces is computed.

If h

This leads to