The $L^p$ CR Hartogs separate analyticity theorem for strictly convex domains

TL;DR

This paper proves a new theorem on CR functions in convex domains in complex space, showing that boundary functions with certain holomorphic extensions are CR, and introduces a new operator limit for the Szegő projection.

Contribution

It establishes an $L^p$ CR Hartogs separate analyticity theorem for convex domains, extending the understanding of CR functions and their holomorphic extensions in complex analysis.

Findings

CR functions on boundary extend holomorphically on slices

New operator limit for Szeg ext{"o} projection

Applicable to a large class of convex domains

Abstract

For a large class of convex domains in $\bf C^n$, it is shown that an $L^p$ function on the boundary is CR if there are holomorphic extensions on almost all slices of D by complex lines parallel to the coordinate axes. As an application, a new operator limit for the Szeg\H{o} projection is obtained.