$L^p$-theory for the tangential Cauchy-Riemann equation

TL;DR

This paper develops an $L^p$-theory for the tangential Cauchy-Riemann operator on certain CR manifolds, establishing isomorphisms and duality results to solve the equation with estimates.

Contribution

It extends the Dolbeault isomorphism and Andreotti-Grauert theory to $L^p$-settings on $s$-concave CR manifolds, providing new solvability results.

Findings

Established $L^p$-Dolbeault isomorphism for CR manifolds.

Developed $L^p$-Andreotti-Grauert theory in this context.

Solved the tangential Cauchy-Riemann equation with $L^p$-estimates and exact support.

Abstract

We are interested in $L^p$-theory for the tangential Cauchy-Riemann operator in locally embeddable, $s$-concave, generic CR manifolds. We study the Dolbeault isomorphism and develop the Andreotti-Grauert theory in that setting. Using Serre duality, we solve the tangential Cauchy-Riemann equation with exact support and $L^p$-estimates.