Boundedness of the Bergman Projection on Generalized Fock–Sobolev Spaces on $${{\mathbb {C}}}^n$$

Abstract

In this paper we solve a problem posed by Bommier-Hato et al. (J Math Anal Appl 389:1086–1104, 2012) on the boundedness of the Bergman-type projections in generalized Fock spaces. It will be a consequence of two facts: a full description of the embeddings between generalized Fock–Sobolev spaces and a complete characterization of the boundedness of the above Bergman type projections between weighted $$L^p$$-spaces related to generalized Fock–Sobolev spaces.