Semigroups of weighted composition operators in spaces of analytic functions

Abstract

We study the strong continuity of weighted composition semigroups of the form $T_{t}f={\phi }_t^{\prime }\left(f\circ {\phi }_t\right)$ in several spaces of analytic functions. First we give a general result on separable spaces and use it to prove that these semigroups are always strongly continuous in the Hardy and Bergman spaces. Then we focus on two non-separable family of spaces, the mixed norm and the weighted Banach spaces. We characterize the maximal subspace in which a semigroup of analytic functions induces a strongly continuous semigroup of weighted composition operators depending on its Denjoy-Wolff point, via the study of an integral-type operator.

Cited by in corpus (1)

• Weighted composition semigroups on some Banach spaces