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

Abstract

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

Minor changes, to appear in Complex Variables and Elliptic Equations