Weighted superposition operators on Fock spaces

Abstract

We characterize all pairs of entire functions $$(u,\psi )$$ ( u , ψ ) for which the induced weighted superposition operator $$S_{(u,\psi )}$$ S ( u , ψ ) transforms one Fock space into another Fock space. Further analytical structures like boundedness and Lipschitz continuity of $$S_{(u,\psi )}$$ S ( u , ψ ) are described. We, in particular, show the Fock spaces support no compact weighted superposition operator.

Integration operators on Hardy-Carleson type tent spaces

“…The theory of superposition operators has a long history in the context of real-valued functions; see [2]. Since the pioneering works of Cámera and Giménez [5,6], the superposition operators on spaces of analytic functions have drawn lots of attention; see [1,14,26,37] and the references therein. However, as far as we know, it seems that the superposition operators have not been studied in the setting of several complex variables.…”