Regularity of infinitesimal CR automorphisms

TL;DR

This paper investigates the smoothness properties of infinitesimal CR automorphisms on abstract CR structures, establishing conditions under which these automorphisms become smooth through specific multipliers, with applications to hypersurfaces of infinite type.

Contribution

It introduces a microlocal extension framework and identifies smooth multipliers that regularize infinitesimal CR automorphisms, advancing understanding of their smoothness behavior.

Findings

Existence of smooth multipliers determined by CR structure

Regularity results for automorphisms of infinite type hypersurfaces

Application to embedded CR structures of infinite type

Abstract

We study the regularity of infinitesimal CR automorphisms of abstract CR structures which possess a certain microlocal extension and show that there are smooth multipliers, completely determined by the CR structure, such that if $X$ is such an infinitesimal CR automorphism, then $\lambda X$ is smooth for all multipliers $\lambda$. As an application, we study the regularity of infinitesimal automorphisms of certain embedded hypersurfaces of infinite type.