Spectral multipliers for sub-Laplacians on solvable extensions of stratified groups |
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| Authors: | Alessio Martini Alessandro Ottazzi Maria Vallarino |
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| Institution: | 1.School of Mathematics,University of Birmingham Edgbaston,Birmingham,United Kingdom;2.School of Mathematics and Statistics,University of New South Wales, UNSW,Sydney,Australia;3.Dipartimento di Scienze Matematiche “Giuseppe Luigi Lagrange”,Politecnico di Torino,Torino,Italy |
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| Abstract: | Let G = N ? A, where N is a stratified group and A = ? acts on N via automorphic dilations. Homogeneous sub-Laplacians on N and A can be lifted to left-invariant operators on G, and their sum is a sub-Laplacian Δ on G. We prove a theorem of Mihlin–Hörmander type for spectral multipliers of Δ. The proof of the theorem hinges on a Calderón–Zygmund theory adapted to a sub-Riemannian structure of G and on L1-estimates of the gradient of the heat kernel associated to the sub-Laplacian Δ. |
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