Cesáro-like operators on the Hardy and Bergman spaces of the half plane

Abstract

We construct integral operators associated with strongly continuous groups of invertible isometries on the Hardy spaces and the weighted Bergman spaces of the upper half plane. Specifically, we obtain the spectrum and point spectrum of the generator and represent resolvents as integral operators related to the Cesàro operator investigated by Arvanitidis and Siskakis

C1f(z):=1z∫z0f(ζ)dζ on the Hardy Spaces Hp(U),p>1, Arvanitidis and Siskakis (Can Math Bull 153:1–12, 2011).