Subelliptic sharp Gårding inequality on compact Lie groups

Abstract

In this work we establish a subelliptic sharp Gårding inequality on compact Lie groups for pseudo-differential operators with symbols belonging to global subelliptic Hörmander classes. In order for the inequality to hold we require the global matrix-valued symbol to satisfy the suitable classical nonnegativity condition in our setting. Our result extends to ${\mathcal{S}}_{\rho ,\delta }^m(G)$-classes, $0\le \delta <\rho$, the one in [26] about the validity of the sharp Gårding inequality for the class ${\mathcal{S}}_{1,0}^m(G)$. We remark that the result we prove here is already new and sharp in the case of the torus.

References in corpus (2)

• Lp Fourier multipliers on compact Lie groups
• Lower bounds for operators on graded Lie groups