Commutators of singular integrals, the Bergman projection, and boundary regularity of elliptic equations in the plane

TL;DR

This paper investigates the behavior of commutators of singular integral operators in Lipschitz spaces and applies these findings to understand boundary regularity of elliptic equations in the plane, including an explicit formula for the Bergman projection.

Contribution

It provides new estimates for commutators of singular integrals and derives an explicit asymptotic formula for the Bergman projection, linking operator theory to boundary regularity.

Findings

Established bounds for commutators in Lipschitz spaces

Derived an explicit asymptotic formula for the Bergman projection

Connected operator estimates to boundary regularity of elliptic PDEs

Abstract

We obtain estimates of commutators of singular integral operators in Lipschitz spaces and apply the results to boundary regularity of elliptic equations in the plane. We obtain an explicit asymptotic formula for the Bergman projection.