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

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 ℓ p (L p ′ ) formés des fonctions appartenant localement à L p ′ et qui ont un comportement ℓ p à l’infini.

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 ℓ p (L p ′ ) of functions belonging locally to L p ′ and with ℓ p behaviour at infinity.

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

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