Sobolev Regularity of Weighted Bergman Projections on the Unit Disc

TL;DR

This paper proves that weighted Bergman projections with radially symmetric weights on the unit disc are bounded operators on Sobolev spaces, extending understanding of their regularity properties.

Contribution

It establishes Sobolev regularity of weighted Bergman projections for radially symmetric weights, a result not previously known.

Findings

Weighted Bergman projections are bounded on Sobolev spaces.

The result applies to radially symmetric weights on the unit disc.

This advances the theory of regularity for weighted Bergman projections.

Abstract

We show that weighted Bergman projections corresponding to radially symmetric weights on the unit disc are bounded on Sobolev spaces.