Principal parts of operators in the dbar-Neumann problem on strictly pseudoconvex non-smooth domains

TL;DR

This paper constructs an explicit integral kernel for the dbar-Neumann operator on non-smooth Henkin-Leiterer domains, enabling the derivation of $L^p$ estimates and advancing understanding of its mapping properties.

Contribution

It provides a new explicit construction of the integral kernel for the dbar-Neumann operator on non-smooth domains, which was not previously available.

Findings

Explicit integral kernel construction for non-smooth domains

Derived $L^p$ estimates for the operator

Enhanced understanding of the operator's mapping properties

Abstract

Our main goal is to describe the integral kernel of the dbar-Neumann operator on certain non-smooth domains, the so-called Henkin-Leiterer domains. We do so by explicitly constructing an integral kernel which accounts for the main mapping properties of the operator. We use our calculations to derive $L^p$ estimates.