Boundedness of the Bergman projection on generalized Fock-Sobolev spaces on ${\mathbb C}^n$

TL;DR

This paper characterizes when Bergman projections are bounded on generalized Fock-Sobolev spaces, providing a comprehensive understanding of embeddings and boundedness criteria in these complex function spaces.

Contribution

It offers a complete description of embeddings and a full characterization of the boundedness of Bergman-type projections in generalized Fock spaces, solving a previously open problem.

Findings

Full description of embeddings between generalized Fock-Sobolev spaces

Complete characterization of boundedness of Bergman projections

Resolved an open problem in the field

Abstract

In this paper we solve a problem posed by H. Bommier-Hato, M. Engli\v{s} and E.H. Youssfi in [3] 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.