Abstract
Let (χ,G, U) be a continuous representation of a Lie groupG by bounded operatorsg ↦U (g) on the Banach space χ and let (χ,\(\mathfrak{g}\),dU) denote the representation of the Lie algebra\(\mathfrak{g}\) obtained by differentiation. Ifa 1, ...,a d′ is a Lie algebra basis of\(\mathfrak{g}\),A i =dU (a i ) and\(A^\alpha = A_{i_1 } ...A_{i_k } \) whenever α=(i 1, ...,i k ) we reconsider the operators
with complex coefficientsc α 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.
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Ter Elst, A.F.M., Robinson, D.W. Subcoercivity and subelliptic operators on Lie groups II: The general case. Potential Anal 4, 205–243 (1995). https://doi.org/10.1007/BF01071695
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DOI: https://doi.org/10.1007/BF01071695