Extended Cesàro companion operators on generalized Fock spaces

Abstract

In this paper we give a characterizations of the bounded and compact extended Cesàro companion operators acting between the generalized Fock spaces. We also obtain asymptotic estimates for the norm of these operators in terms of certain integral transforms, which are related to some function-theoretic properties of the symbols that induce the operators. As an application, we prove that there exist no nontrivial compact extended Cesàro companion integral and multiplication operators on generalized Fock spaces.