Analysis of joint spectral multipliers on Lie groups of polynomial growth
Annales de l'Institut Fourier, Volume 62 (2012) no. 4, p. 1215-1263

We study the problem of L p -boundedness (1<p<) of operators of the form m(L 1 ,,L n ) for a commuting system of self-adjoint left-invariant differential operators L 1 ,,L n on a Lie group G of polynomial growth, which generate an algebra containing a weighted subcoercive operator. In particular, when G is a homogeneous group and L 1 ,,L n are homogeneous, we prove analogues of the Mihlin-Hörmander and Marcinkiewicz multiplier theorems.

On étudie la bornitude L p (1<p<) des opérateurs de la forme m(L 1 ,,L n ) pour un système commutatif L 1 ,,L n d’opérateurs différentiels autoadjoints invariants à gauche sur un groupe de Lie G à croissance polynomiale, qui engendrent une algèbre contenant un opérateur sous-coercif pondéré. En particulier, quand G est un groupe homogène et L 1 ,,L n sont homogènes, on prouve des analogues des theorèmes de multiplicateurs de Mihlin-Hörmander et Marcinkiewicz.

DOI : https://doi.org/10.5802/aif.2721
Classification:  43A22,  22E30,  42B15
Keywords: spectral multipliers, joint functional calculus, differential operators, Lie groups, polynomial growth, singular integral operators
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {62},
     number = {4},
     year = {2012},
     pages = {1215-1263},
     doi = {10.5802/aif.2721},
     mrnumber = {3025742},
     zbl = {1255.43003},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2012__62_4_1215_0}
}
Martini, Alessio. Analysis of joint spectral multipliers on Lie groups of polynomial growth. Annales de l'Institut Fourier, Volume 62 (2012) no. 4, pp. 1215-1263. doi : 10.5802/aif.2721. http://www.numdam.org/item/AIF_2012__62_4_1215_0/

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