Essential norm and a new characterization of weighted composition operators from weighted Bergman spaces and Hardy spaces into the Bloch space

TL;DR

This paper provides estimates for the essential norm and introduces a new way to characterize when weighted composition operators are bounded or compact from weighted Bergman and Hardy spaces into the Bloch space.

Contribution

It offers novel estimates for the essential norm and a new characterization of boundedness and compactness for weighted composition operators between these function spaces.

Findings

Derived estimates for the essential norm of the operators.

Established a new characterization criterion for boundedness.

Provided conditions for compactness of the operators.

Abstract

In this paper, we give some estimates for the essential norm and a new characterization for the boundedness and compactness of weighted composition operators from weighted Bergman spaces and Hardy spaces to the Bloch space.