Unions et intersections d’espaces L p invariantes par translation ou convolution
Annales de l'Institut Fourier, Volume 28 (1978) no. 2, p. 53-84

This paper is concerned with properties of unions and intersections of L p (s) spaces where s belongs to a set S of positive measures on a locally compact abelian group and where S is translation invariant or convolution invariant.

In special cases, we find again properties of spaces studied by A. Beurling and by B. Koremblium.

We also study the spaces p (L p ) of functions belonging locally to L p and with p behaviour at infinity.

Étude des propriétés des unions et intersections d’espaces L p (s) relatifs à un ensemble S de mesures positives sur un groupe commutatif localement compact lorsque S est invariant par translation ou stable par convolution.

Dans des cas particuliers, on retrouve les propriétés d’espaces étudiés par A. Beurling et par B. Koremblium.

On étudie aussi les espaces p (L p ) formés des fonctions appartenant localement à L p et qui ont un comportement p à l’infini.

@article{AIF_1978__28_2_53_0,
     author = {Bertrandias, Jean-Paul and Datry, Christian and Dupuis, Christian},
     title = {Unions et intersections d'espaces $L^p$ invariantes par translation ou convolution},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {28},
     number = {2},
     year = {1978},
     pages = {53-84},
     doi = {10.5802/aif.689},
     zbl = {0365.46029},
     mrnumber = {81g:43005},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1978__28_2_53_0}
}
Bertrandias, Jean-Paul; Datry, Christian; Dupuis, Christian. Unions et intersections d’espaces $L^p$ invariantes par translation ou convolution. Annales de l'Institut Fourier, Volume 28 (1978) no. 2, pp. 53-84. doi : 10.5802/aif.689. http://www.numdam.org/item/AIF_1978__28_2_53_0/

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