Spectral multipliers for sub-Laplacians on solvable extensions of stratified groups

Alessio Martini, Alessandro Ottazzi, Maria Vallarino

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Abstract

Let G = N ⋊ A, where N is a stratified group and A = ℝ 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.
Original languageEnglish
Pages (from-to)357-397
Number of pages41
JournalJournal d'Analyse Mathématique
Volume136
Issue number1
DOIs
Publication statusPublished - 1 Oct 2018

Bibliographical note

Acceptance date: 25/09/2015

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