Volterra operators and semigroups in weighted Banach spaces of analytic functions

Abstract

We characterize the boundedness, compactness and weak compactness of Volterra operators Vg(f)(z) {colon equals} ∫z0 f(ζ)g′(ζ)dζ acting between different weighted spaces of type H∞v in terms of the symbol function g, for the case when v is a quasi-normal weight, a notion weaker than normality. Then we apply the characterization of compactness to analyze the behavior of semigroups of composition operators on H∞v. © 2013 Universitat de Barcelona.