Spectral multipliers on lie groups of polynomial growth
AuthorAlexopoulos, Georgios K.
SourceProceedings of the American Mathematical Society
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Let L be a left invariant sub-Laplacian on a connected Lie group G of polynomial volume growth, and let (Eγγ ≥ 0) be the spectral resolution of L and m a bounded Borel measurable function on [0, ∞). In this article we give a sufficient condition on m for the operator to extend to an operator bounded on LP(G), 1 < p < ∞, and also from L1(G) to weak-L-1(G). © 1994 American Mathematical Society.