The Kohn-H\"ormander-Morrey formula twisted by a pseudodifferential operator

TL;DR

This paper extends the Kohn-H"ormander-Morrey formula using pseudodifferential operators and demonstrates its application in identifying new domains where the $ar ext{ extlambda}$-Neumann problem is locally hypoelliptic.

Contribution

It introduces a generalized weighted Kohn-H"ormander-Morrey formula twisted by pseudodifferential operators and applies it to find new classes of domains with hypoelliptic $ar ext{ extlambda}$-Neumann problems.

Findings

Established a generalized weighted Kohn-H"ormander-Morrey formula with pseudodifferential operators.

Identified new domain classes where the $ar ext{ extlambda}$-Neumann problem is locally hypoelliptic.

Demonstrated the practical application of the formula in complex analysis.

Abstract

We establish a general, weighted Kohn-H\"ormander-Morrey formula twisted by a pseudodifferential operator. As an application, we exhibit a new class of domains for which the $\bar\partial$-Neumann problem is locally hypoelliptic.