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arXiv · 2208.06241

Variable Lebesgue algebra on a Locally Compact group

Parthapratim Saha·Bipan Hazarika
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Abstract

For a locally compact group $H$ with a left Haar measure, we study variable Lebesgue algebra $\mathcal{L}^{p(\cdot)}(H)$ with respect to a convolution. We show that if $\mathcal{L}^{p(\cdot)}(H)$ has 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.

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BibTeXRIS

Parthapratim Saha, Bipan Hazarika. 2022-08-11. Variable Lebesgue algebra on a Locally Compact group. https://arxiv.org/abs/2208.06241

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