On étudie la bornitude () des opérateurs de la forme pour un système commutatif d’opérateurs différentiels autoadjoints invariants à gauche sur un groupe de Lie à croissance polynomiale, qui engendrent une algèbre contenant un opérateur sous-coercif pondéré. En particulier, quand est un groupe homogène et sont homogènes, on prouve des analogues des theorèmes de multiplicateurs de Mihlin-Hörmander et Marcinkiewicz.
We study the problem of -boundedness () of operators of the form for a commuting system of self-adjoint left-invariant differential operators on a Lie group of polynomial growth, which generate an algebra containing a weighted subcoercive operator. In particular, when is a homogeneous group and are homogeneous, we prove analogues of the Mihlin-Hörmander and Marcinkiewicz multiplier theorems.
Keywords: spectral multipliers, joint functional calculus, differential operators, Lie groups, polynomial growth, singular integral operators
Mot clés : multiplicateurs spectraux, calcul fonctionnel conjoint, opérateurs différentiels, groupes de Lie, croissance polynomiale, opérateurs intégraux singuliers
@article{AIF_2012__62_4_1215_0, author = {Martini, Alessio}, title = {Analysis of joint spectral multipliers on {Lie} groups of polynomial growth}, journal = {Annales de l'Institut Fourier}, pages = {1215--1263}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {62}, number = {4}, year = {2012}, doi = {10.5802/aif.2721}, zbl = {1255.43003}, mrnumber = {3025742}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2721/} }
TY - JOUR AU - Martini, Alessio TI - Analysis of joint spectral multipliers on Lie groups of polynomial growth JO - Annales de l'Institut Fourier PY - 2012 SP - 1215 EP - 1263 VL - 62 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2721/ DO - 10.5802/aif.2721 LA - en ID - AIF_2012__62_4_1215_0 ER -
%0 Journal Article %A Martini, Alessio %T Analysis of joint spectral multipliers on Lie groups of polynomial growth %J Annales de l'Institut Fourier %D 2012 %P 1215-1263 %V 62 %N 4 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2721/ %R 10.5802/aif.2721 %G en %F AIF_2012__62_4_1215_0
Martini, Alessio. Analysis of joint spectral multipliers on Lie groups of polynomial growth. Annales de l'Institut Fourier, Tome 62 (2012) no. 4, pp. 1215-1263. doi : 10.5802/aif.2721. http://www.numdam.org/articles/10.5802/aif.2721/
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