Subcoercivity and subelliptic operators on Lie groups II

Abstract

Let (χ, G, U) be a continuous representation of a Lie group G by bounded operators g {mapping}U (g) on the Banach space χ and let (χ, {Mathematical expression}, dU) denote the representation of the Lie algebra {Mathematical expression} obtained by differentiation. If a1, ..., ad′ is a Lie algebra basis of {Mathematical expression}, Ai=dU (ai) and {Mathematical expression} whenever α=(i1, ..., ik) we reconsider the operators {Mathematical expression} with complex coefficients cα satisfying a subcoercivity condition previously analyzed on stratified groups [3]. All the earlier results are extended to general groups by combination of embedding arguments and parametrices. Show more