Multiplicateurs de Mikhlin pour une classe particulière de groupes non-unimodulaires

Mustapha, Sami

Annales de l'Institut Fourier, Tome 48 (1998), p. 957-966 / Harvested from Numdam

Résumé

On montre, pour une classe particulière de groupes non-unimodulaires $G=N\rightthreetimes {\Bbb R}$, où $N$ est un groupe de Lie stratifié et où l’action de ${\Bbb R}$ est définie par les dilatations naturelles de $N$, et pour les sous-laplaciens invariants à gauche correspondants $\Delta $, que toute fonction $m\in H^{2+\epsilon }({\Bbb R})$ possédant un support compact dans ${\Bbb R}_+$ définit un opérateur $m(\Delta )$ borné sur les espaces de Lebesgue $L^p(G,d^rg)$ associés à la mesure de Haar invariante à droite sur $G$, $1\le p \le \infty $.

Abstract

For a particular class of non-unimodular Lie groups $G=N\rightthreetimes {\Bbb R}$, where $N$ is a stratified group and the action of ${\Bbb R}$ being defined by the natural dilations on $N$ and for corresponding left invariant sub-Laplacians $\Delta $, we prove that functions $m\in H^{2+\epsilon }({\Bbb R})$ with compact support in ${\Bbb R}_+$ give spectral bounded multipliers on the Lebesgue spaces $L^p(G,d^rg)$ taken with respect to the right-invariant Haar measure on $G$, $1\le p\le \infty $.

Détail

Publié le : 1998-01-01

MR 99j:22013 | Zbl 0911.22002

DOI : https://doi.org/10.5802/aif.1644

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