Regularity at the Boundary and Tangential Regularity

TL;DR

This paper establishes the equivalence of boundary and interior hypoellipticity for pseudoconvex domains in complex space, advancing the understanding of regularity properties using holomorphic extension techniques.

Contribution

It introduces a new approach replacing harmonic extension with holomorphic extension to prove boundary and interior hypoellipticity equivalence.

Findings

Proves equivalence of hypoellipticity systems in boundary and interior

Develops a new holomorphic extension method for regularity analysis

Advances theoretical understanding of boundary regularity in complex analysis

Abstract

For a pseudoconvex domain in complex space, we prove the equivalence of the local hypoellipticity of the system (di-bar, di-bar*) with the system (di-bar_b,di-bar*_b) induced in the boundary. This develops a result of ours which used the theory of the "harmonic" extension by Kohn. This technique is inadequate for the purpose of the present paper and must be replaced by the "holomorphic" extension introduced by the authors in former work.