Subelliptic Gevrey spaces

TL;DR

This paper introduces and analyzes Gevrey spaces linked to sub-Laplacians generated by H"ormander vector fields, exploring their properties on manifolds, Lie groups, and specific cases like the Heisenberg group and SU(2).

Contribution

It defines new Gevrey spaces associated with sub-Laplacians and establishes their relations across different geometric settings, including Lie groups and specific examples.

Findings

Gevrey spaces relations on general manifolds

Coincidence of definitions on Heisenberg group and SU(2)

Properties on Lie groups with polynomial volume growth

Abstract

In this paper, we define and study Gevrey spaces associated with a H\"ormander family of (globally defined) vector fields and its corresponding sub-Laplacian. We show some natural relations between the various Gevrey spaces in this setting on general manifolds, and more particular properties on Lie groups with polynomial growth of the volume. In the case of the Heisenberg group and of $SU(2)$, we show that all our descriptions coincide.