Functional analysis
Periodic Fourier integral operators in L p -spaces
Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 547-553.

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].

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].

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DOI: 10.5802/crmath.194
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
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Cardona, Duván; Messiouene, Rekia; Senoussaoui, Abderrahmane. Periodic Fourier integral operators in $L^p$-spaces. Comptes Rendus. Mathématique, Volume 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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