[Multiplicateurs pour les espaces de Besov sur les groupes de Lie gradués]
Dans cette note, nous étudions des espaces de Besov sur les groupes de Lie gradués et nous prouvons des théorèmes de multiplicateurs spectraux et de Fourier sur ces groupes. Nous présentons aussi une inégalité de type Nikolskii et le théorème de Littlewood–Paley, qui jouent un rôle dans cette analyse et sont également d'intérêt indépendant.
In this note, we give embeddings and other properties of Besov spaces, as well as spectral and Fourier multiplier theorems, in the setting of graded Lie groups. We also present a Nikolskii-type inequality and the Littlewood–Paley theorem that play a role in this analysis and are also of interest on their own.
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@article{CRMATH_2017__355_4_400_0,
author = {Duv\'an Cardona and Michael Ruzhansky},
title = {Multipliers for {Besov} spaces on graded {Lie} groups},
journal = {Comptes Rendus. Math\'ematique},
pages = {400--405},
publisher = {Elsevier},
volume = {355},
number = {4},
year = {2017},
doi = {10.1016/j.crma.2017.02.015},
language = {en},
}
Duván Cardona; Michael Ruzhansky. Multipliers for Besov spaces on graded Lie groups. Comptes Rendus. Mathématique, Volume 355 (2017) no. 4, pp. 400-405. doi : 10.1016/j.crma.2017.02.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.02.015/
[1] Fourier multipliers and group von Neumann algebras, C. R. Acad. Sci. Paris, Ser. I, Volume 354 (2016), pp. 766-770
[2] Spectral multipliers on Lie groups of polynomial growth, Proc. Amer. Math. Soc., Volume 120 (1994), pp. 973-979
[3] Espaces de Besov et estimations de Strichartz généralisées sur le groupe de Heisenberg, J. Anal. Math., Volume 82 (2000), pp. 93-118
[4] Fourier multipliers on graded Lie groups | arXiv
[5] Quantization on Nilpotent Lie Groups, Prog. Math., vol. 314, Birkhäuser, 2016 (Open access book)
[6] Sobolev spaces on graded groups, Ann. Inst. Fourier (2017) (in press) | arXiv
[7] Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat., Volume 13 (1975), pp. 161-207
[8] Hardy Spaces on Homogeneous Groups, Mathematical Notes, vol. 28, Princeton University Press/University of Tokyo Press, Princeton, NJ/Tokyo, 1982
[9] Littlewood–Paley decompositions and Besov spaces on Lie groups of polynomial growth, Math. Nachr., Volume 279 (2006) no. 9–10, pp. 1028-1040
[10] Liouville's theorem for homogeneous groups, Commun. Partial Differ. Equ., Volume 8 (1983), pp. 1665-1677
[11] Caractérisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe de Lie nilpotent gradué, Commun. Partial Differ. Equ., Volume 4 (1979), pp. 899-958
[12] Inequalities for entire functions of finite degree and their applications in the theory of differentiable functions of many variables, Proc. Steklov Inst. Math., Volume 38 (1951), pp. 244-278
[13] Nikolskii inequality and Besov, Triebel–Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds, Ann. Sc. Norm. Super. Pisa, Cl. Sci., Volume XVI (2016), pp. 981-1017 | arXiv
[14] Bernstein–Nikolskii and Plancherel–Polya inequalities in Lp-norms on non-compact symmetric spaces, Math. Nachr. (2), Volume 282 (2009), pp. 253-269
[15] Hypoelliptic differential operators and nilpotent groups, Acta Math., Volume 137 (1976), pp. 247-320
[16] Besov spaces and Sobolev spaces on a nilpotent Lie group, Tóhoku Math. J. (2), Volume 31 (1979) no. 4, pp. 383-437
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