On the norm and the essential norm of weighted composition operators acting on the weighted Banach space of analytic functions

Abstract

The objective of this paper is to use known properties of the associated weight to give new estimations of the norm and essential norm of the weighted composition operators acting between weighted Banach spaces of analytic functions, in terms of composition with certain special functions in these spaces. As a consequence of our results, we obtain genuine extensions of a large number of recent results, and in particular, we extend classical results due to Montes-Rodríguez and Contreras and Hernández-Díaz.

Keywords: Weighted Banach spaces of analytic functions, Bloch space, weighted composition operators