$L^p$ Regularity of Weighted Szeg\"o Projections on the Unit Disc

TL;DR

This paper explores the irregularity of weighted Szeg"o projection operators on the unit disc for certain weights and examines the dual spaces of related weighted Hardy spaces.

Contribution

It introduces a specific family of weights causing irregularity in Szeg"o projections and analyzes the dual spaces of associated weighted Hardy spaces.

Findings

Identification of weights causing irregularity in Szeg"o projections

Analysis of dual spaces of weighted Hardy spaces

Insights into $L^p$ regularity issues for weighted projections

Abstract

We present a family of weights on the unit disc for which the corresponding weighted Szeg\"o projection operators are irregular on $L^p$ spaces. We further investigate the dual spaces of weighted Hardy spaces corresponding to this family.