A note on smoothing properties of the Bergman projection

TL;DR

This paper demonstrates that on certain Reinhardt domains, the Bergman projection of conjugate holomorphic functions extends holomorphically beyond the boundary, revealing a new smoothing property.

Contribution

It establishes a novel smoothing property of the Bergman projection on Reinhardt domains, extending previous boundary regularity results to holomorphic extension beyond the boundary.

Findings

Bergman projection of conjugate holomorphic functions is smooth up to the boundary.

On Reinhardt domains, the projection extends holomorphically past the boundary.

The result generalizes previous boundary regularity findings.

Abstract

Recently Herbig, McNeal, and Straube have showed that the Bergman projection of conjugate holomorphic functions is smooth up to the boundary on a class of pseudoconvex domains. We show that a further smoothing property holds on a family of Reinhardt domains; namely, the Bergman projection of conjugate holomorphic functions is holomorphic past the boundary.