Unions et intersections d’espaces L p invariantes par translation ou convolution

Jean-Paul Bertrandias; Christian Datry; Christian Dupuis

Annales de l'institut Fourier (1978)

  • Volume: 28, Issue: 2, page 53-84
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Bertrandias, Jean-Paul, Datry, Christian, and Dupuis, Christian. "Unions et intersections d’espaces $L^p$ invariantes par translation ou convolution." Annales de l'institut Fourier 28.2 (1978): 53-84. <http://eudml.org/doc/74361>.

@article{Bertrandias1978,
abstract = {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 $\ell ^p(L^\{p^\{\prime \}\})$ formés des fonctions appartenant localement à $L^\{p^\{\prime \}\}$ et qui ont un comportement $\ell ^p$ à l’infini.},
author = {Bertrandias, Jean-Paul, Datry, Christian, Dupuis, Christian},
journal = {Annales de l'institut Fourier},
language = {fre},
number = {2},
pages = {53-84},
publisher = {Association des Annales de l'Institut Fourier},
title = {Unions et intersections d’espaces $L^p$ invariantes par translation ou convolution},
url = {http://eudml.org/doc/74361},
volume = {28},
year = {1978},
}

TY - JOUR
AU - Bertrandias, Jean-Paul
AU - Datry, Christian
AU - Dupuis, Christian
TI - Unions et intersections d’espaces $L^p$ invariantes par translation ou convolution
JO - Annales de l'institut Fourier
PY - 1978
PB - Association des Annales de l'Institut Fourier
VL - 28
IS - 2
SP - 53
EP - 84
AB - 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 $\ell ^p(L^{p^{\prime }})$ formés des fonctions appartenant localement à $L^{p^{\prime }}$ et qui ont un comportement $\ell ^p$ à l’infini.
LA - fre
UR - http://eudml.org/doc/74361
ER -

References

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  1. [1] L. N. ARGABRIGHT and J. GIL DE LAMADRID, Fourier analysis of unbounded measures on locally compact abelian groups, Memoirs of the Ann. Math. Soc., n° 145 (1974). Zbl0294.43002MR58 #29842
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