Geodesic
Variable Lebesgue algebra on a Locally Compact group
Problemy analiza, Tome 12 (2023) no. 1, pp. 34-45

Voir la notice de l'article provenant de la source Math-Net.Ru

For a locally compact group $H$ with a left Haar measure, we study the variable Lebesgue algebra $\mathcal{L}^{p(\cdot)}(H)$ with respect to convolution. We show that if $\mathcal{L}^{p(\cdot)}(H)$ has a bounded exponent, then it contains a left approximate identity. We also prove a necessary and sufficient condition for $\mathcal{L}^{p(\cdot)}(H)$ to have an identity. We observe that a closed linear subspace of $\mathcal{L}^{p(\cdot)}(H)$ is a left ideal if and only if it is left translation invariant.
Mots-clés : variable Lebesgue space
Keywords: bounded exponent, approximate identity, Haar measure. 
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     author = {P. Saha and B. Hazarika},
     title = {Variable {Lebesgue} algebra on a {Locally} {Compact} group},
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P. Saha; B. Hazarika. Variable Lebesgue algebra on a Locally Compact group. Problemy analiza, Tome 12 (2023) no. 1, pp. 34-45. http://geodesic.mathdoc.fr/item/PA_2023_12_1_a2/