$L^p$ Mapping Properties for the Cauchy-Riemann Equations on Lipschitz Domains Admitting Subelliptic Estimates

TL;DR

This paper investigates the boundedness of the $ar{ abla}$-Neumann operators on Lipschitz pseudoconvex domains with good weights, establishing $L^p$ bounds for certain $p > 2$, advancing understanding of regularity in complex analysis.

Contribution

It demonstrates $L^p$ boundedness of the $ar{ abla}$-Neumann operators on Lipschitz pseudoconvex domains with subelliptic estimates, extending previous results to less smooth domains.

Findings

Boundedness of $N_q, ar{ abla}^* N_q, ar{ abla} N_q$ on $L^p$ for some $p > 2

Applicable to Lipschitz pseudoconvex domains with good weight functions

Advances regularity theory for the $ar{ abla}$-problem in non-smooth domains

Abstract

We show that on bounded Lipschitz pseudoconvex domains that admit good weight functions the $\overline{\partial}$-Neumann operators $N_q, \overline{\partial}^* N_{q}$, and $\overline{\partial} N_{q}$ are bounded on $L^p$ spaces for some values of $p$ greater than 2.