Multipliers for Besov spaces on graded Lie groups

Duván Cardona; Michael Ruzhansky

doi:10.1016/j.crma.2017.02.015

Mathematical analysis/Harmonic analysis

Multipliers for Besov spaces on graded Lie groups

Presented by: the Editorial Board

Duván Cardona ¹; Michael Ruzhansky ²

¹ Mathematics Department, Universidad de los Andes, Carrera 1 No. 18a 10, Bogotá, Colombia
² Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, United Kingdom

Comptes Rendus. Mathématique, Volume 355 (2017) no. 4, pp. 400-405.

Abstract
Résumé

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.

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.

Received: 2016-10-31
Accepted: 2017-02-22
Published online: 2017-03-11

DOI: 10.1016/j.crma.2017.02.015

Author's affiliations:

Duván Cardona ¹; Michael Ruzhansky ²

¹ Mathematics Department, Universidad de los Andes, Carrera 1 No. 18a 10, Bogotá, Colombia
² Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, United Kingdom

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     title = {Multipliers for {Besov} spaces on graded {Lie} groups},
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     pages = {400--405},
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     year = {2017},
     doi = {10.1016/j.crma.2017.02.015},
     language = {en},
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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/

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