Variable Lebesgue algebra on a Locally Compact group

P. Saha ; B. Hazarika

Problemy analiza, Tome 12 (2023) no. 1, pp. 34-45.

Résumé

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.

Détail

Mots-clés : variable Lebesgue space
Keywords: bounded exponent, approximate identity, Haar measure.

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