This paper is concerned with properties of unions and intersections of spaces where belongs to a set of positive measures on a locally compact abelian group and where 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 of functions belonging locally to and with behaviour at infinity.
Étude des propriétés des unions et intersections d’espaces relatifs à un ensemble de mesures positives sur un groupe commutatif localement compact lorsque 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 formés des fonctions appartenant localement à et qui ont un comportement 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{\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/} }
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 SP - 53 EP - 84 VL - 28 IS - 2 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.689/ DO - 10.5802/aif.689 LA - fr ID - AIF_1978__28_2_53_0 ER -
%0 Journal Article %A Bertrandias, Jean-Paul %A Datry, Christian %A Dupuis, Christian %T Unions et intersections d’espaces $L^p$ invariantes par translation ou convolution %J Annales de l'Institut Fourier %D 1978 %P 53-84 %V 28 %N 2 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.689/ %R 10.5802/aif.689 %G fr %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.689/
[1] Fourier analysis of unbounded measures on locally compact abelian groups, Memoirs of the Ann. Math. Soc., n° 145 (1974). | MR | Zbl
and ,[2] The spaces Lp, with mixed norm, Duke Math. J., 28 (1961), 301-324. | Zbl
and ,[3] Potential theory on locally compact abelian groups, Springer 1975. | MR | Zbl
and ,[4] Unions et intersections d'espaces Lp sur un espace localement compact, Bull. Sc. Math., 101 (1977). | MR | Zbl
,[5] Transformation de Fourier sur les espace lp(Lp'), Ann. Inst. Fourier 29 (1979). | Numdam | MR | Zbl
et ,[6] Construction and analysis of some convolution algebras, Ann. Inst. Fourier, 14 (1964), 1-32. | Numdam | MR | Zbl
,[7] Topological Riesz spaces and measure theory, Cambridge, 1974. | MR | Zbl
,[8] On a space of functions of Wiener, Duke Math. J., 34 (1967), 683-691. | MR | Zbl
,[9] A survey of abstract harmonic analysis, dans : Some aspects of analysis and probability, Wiley & sons, 1958. | MR | Zbl
,[10] Abstract harmonic analysis. 2 volumes, Springer, 1963 et 1970.
and ,[11] Harmonic analysis on amalgams of Lp and Lq, J. London Math. Soc., 2, 10 (1975), 295-305. | MR | Zbl
,[12] On certain special commutative normed rings. (en russe), Doklady Akad. Nauk SSSR, 64 (1949), 281-284.
,[13] Measures with separable orbits, Proc. Am. Math. Soc., 19 (1968), 569-572. | MR | Zbl
,[14] Classical harmonic analysis and locally compact groups, Clarendon Press, Oxford, 1968. | MR | Zbl
,[15] L1-algebras and Segal algebras, Lectures Notes n° 231, Springer 1971. | MR | Zbl
,[16] Measures algebras on abelian groups, Bull. Am. Math. Soc., 65 (1959), 227-247. | MR | Zbl
,[17] On functions and measures whose Fourier transforms are functions, Math. Ann., 179 (1968), 31-41. | MR | Zbl
,[18] Tauberian theorems, Ann. of Math., 33 (1932), 1-100. | JFM | Zbl
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