Norm of a Volterra Integral Operator on Some Analytic Function Spaces

Hao Li,Songxiao Li

doi:10.1155/2013/492052

Hao Li, Songxiao Li

Open Access

https://doi.org/10.1155/2013/492052

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Abstract

Let f be an analytic function in the unit disc 𝔻. The Volterra integral operator If is defined as follows: If(h)(z)=∫0zf(w)h'(w)dw,h∈H(𝔻),z∈𝔻. In this paper, we compute the norm of If on some analytic function spaces.

Highlights

Let D = {z : |z| < 1} be the unit disk of complex plane C and H(D) the class of functions analytic in D
From [1, 2], we see that Q1 = BMOA, the space of all analytic functions of bounded mean oscillation
Liu and Xiong studied the norm of integral operators If and Jf on the Bloch space, Dirichlet space, BMOA space, and so on in [13]

Summary

Introduction

Let f be an analytic function in the unit disc D. We compute the norm of If on some analytic function spaces. The Qp is the space of all functions f ∈ H(D) such that From [1, 2], we see that Q1 = BMOA, the space of all analytic functions of bounded mean oscillation.

Results

Conclusion