Weighted composition operators from weighted Bergman spaces with Békollé weights to Bloch-type spaces

Stevo Stević,Ajay K Sharma

doi:10.1186/s13660-015-0858-2

Abstract

Let σ be a Bekolle weight function and ν be a weight function. In this paper, we characterize the boundedness and compactness of weighted composition operators acting from Bergman-type spaces $A^{p}(\sigma)$ to Bloch-type spaces $\mathcal{B}_{\nu}$ and $\mathcal{B}_{\nu, 0}$ , considerably extending some results in the literature.

Highlights

Introduction and preliminaries LetD denote the open unit disk in the complex plane C, H(D) the space of all holomorphic functions on D, and S(D) the class of all holomorphic self-maps of D
Let ψ ∈ H(D) and φ ∈ S(D), the weighted composition operator Wψ,φ is a linear operator on H(D) defined by
It is of interest to provide function-theoretic characterizations when symbols φ and ψ induce a bounded or compact weighted composition operator between different function spaces

Summary

Introduction

Introduction and preliminaries LetD denote the open unit disk in the complex plane C, H(D) the space of all holomorphic functions on D, and S(D) the class of all holomorphic self-maps of D. Lemma Let ν be a standard weight.

Results

Conclusion