Properties of β-cesàro operators on α-bloch space

Abstract

For each α > 0, the α-Bloch space consists of all analytic functions f on the unit disk satisfying supjzj<1.1 - jzj2/αj f 0.z/j < +∞. We consider the following complex integral operators, namely the β-Cesàro operator (equation presented) and its generalization, acting from the α-Bloch space to itself, where f .0/ D 0 and β ∈ R. We investigate the boundedness and compactness of the β-Cesàro operators and their generalizations. Also we calculate the essential norm and spectrum of these operators. © 2020 Rocky Mountain Mathematics Consortium. All rights reserved.