Regularity of infinitesimal CR automorphisms

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 $λX$ is smooth for all multipliers $λ$. As an application, we study the regularity of infinitesimal automorphisms of certain embedded hypersurfaces of infinite type.

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