Nous considérons une certaine classe de groupes de Lie (non-unimodulaires) de type NA de rang un avec des racines non toutes positives, et nous montrons que, sur chacun de ces groupes, il existe un sous-laplacien invariant à gauche particulier qui admet un calcul fonctionnel Lp-différentiable pour tout p∈[1,+∞].
We consider a particular class of (non-unimodular) rank one NA-groups with roots not all positive, and we show that, on each of these groups, there exists a distinguished left invariant sub-Laplacian which admits a Lp-differentiable functional calculus for every p∈[1,+∞].
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Emilie David-Guillou 1
@article{CRMATH_2003__337_12_767_0, author = {Emilie David-Guillou}, title = {Spectral multipliers on some rank one {\protect\emph{NA}-groups} with roots not all positive}, journal = {Comptes Rendus. Math\'ematique}, pages = {767--770}, publisher = {Elsevier}, volume = {337}, number = {12}, year = {2003}, doi = {10.1016/j.crma.2003.10.020}, language = {en}, }
Emilie David-Guillou. Spectral multipliers on some rank one NA-groups with roots not all positive. Comptes Rendus. Mathématique, Volume 337 (2003) no. 12, pp. 767-770. doi : 10.1016/j.crma.2003.10.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.10.020/
[1] On Lp spectral multipliers for a solvable Lie group, Geom. Funct. Anal., Volume 6 (1996) no. 5, pp. 860-876
[2] Boundedness of L1 spectral multipliers for an exponential solvable Lie group, Colloq. Math., Volume 73 (1997) no. 1, pp. 155-164
[3] Spectral multipliers on metabelian groups, Rev. Mat. Iberoamericana, Volume 16 (2000) no. 3, pp. 597-604
[4] Estimates for translation invariant operators in Lp spaces, Acta Math., Volume 104 (1960), pp. 93-140
[5] Sub-Laplacians of holomorphic Lp-type on rank one AN-groups and related solvable groups, J. Funct. Anal., Volume 170 (2000) no. 2, pp. 366-427
[6] Multiplicateurs de Mikhlin pour une classe particulière de groupes non-unimodulaires, Ann. Inst. Fourier (Grenoble), Volume 48 (1998) no. 4, pp. 957-966
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