no. 2
Completely continuous multipliers from L 1 (G) into L ∞ (G)
Annales de l'Institut Fourier, Tome 34 (1984) no. 2, pp. 137-154

For a locally compact Hausdorff group G we investigate what functions in L ∞ (G) give rise to completely continuous multipliers T g from L 1 (G) into L ∞ (G). In the case of a metrizable group we obtain a complete description of such functions. In particular, for G compact all g in L ∞ (G) induce completely continuous T g .

Étant donné un groupe G localement compact et séparé, nous étudions les fonctions g de L ∞ (G) qui induisent des convoluteurs T g complètement continus de L 1 (G) dans L ∞ (G). Dans le cas d’un groupe métrisable nous obtenons une description complète de ces fonctions.

@article{AIF_1984__34_2_137_0,
     author = {Crombez, G. and Govaerts, Willy},
     title = {Completely continuous multipliers from $L_1(G)$ into $L_\infty (G)$},
     journal = {Annales de l'Institut Fourier},
     pages = {137--154},
     year = {1984},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {34},
     number = {2},
     doi = {10.5802/aif.968},
     mrnumber = {86b:43003},
     zbl = {0518.42009},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.968/}
}
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Crombez, G.; Govaerts, Willy. Completely continuous multipliers from $L_1(G)$ into $L_\infty (G)$. Annales de l'Institut Fourier, Tome 34 (1984) no. 2, pp. 137-154. doi: 10.5802/aif.968

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