Periodic Fourier integral operators in $L^p$-spaces

Cardona, Duván; Messiouene, Rekia; Senoussaoui, Abderrahmane

doi:10.5802/crmath.194

Analyse fonctionnelle

Periodic Fourier integral operators in

L^{p}

-spaces

Cardona, Duván ¹ ; Messiouene, Rekia ² ; Senoussaoui, Abderrahmane ²

¹ Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, Building S8, Ghent, Belgium
² Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran 1, Ahmed Ben Bella. B.P. 1524 El M’naouar, Oran, Algeria

Comptes Rendus. Mathématique, Tome 359 (2021) no. 5, pp. 547-553.

Résumé
Abstract

Dans cette note nous présentons les conditions suffisantes pour la continuité des opérateurs intégraux de Fourier périodique qui sont appelés aussi séries des opérateurs de Fourier. Le principal outil est la notion des opérateurs intégraux de Fourier et l’analyse discrête notamment l’analyse périodique dans le tore introduite par Ruzhansky et Turunen [34].

In this note we give sufficient conditions for the $L^{p}$ boundedness of periodic Fourier integral operators. We also refer to them as Fourier series operators (FSOs). The main tool will be the notion of full symbol and the periodic analysis on the torus introduced by Ruzhansky and Turunen [34].

Reçu le : 2019-02-15
Révisé le : 2020-07-25
Accepté le : 2021-02-19
Publié le : 2021-07-13

DOI : 10.5802/crmath.194

Affiliations des auteurs :

Cardona, Duván ¹ ; Messiouene, Rekia ² ; Senoussaoui, Abderrahmane ²

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     title = {Periodic {Fourier} integral operators in $L^p$-spaces},
     journal = {Comptes Rendus. Math\'ematique},
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Cardona, Duván; Messiouene, Rekia; Senoussaoui, Abderrahmane. Periodic Fourier integral operators in $L^p$-spaces. Comptes Rendus. Mathématique, Tome 359 (2021) no. 5, pp. 547-553. doi : 10.5802/crmath.194. http://www.numdam.org/articles/10.5802/crmath.194/

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