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arXiv · 2501.05895

Continuous field of Orlicz space on locally compact groupoids and related results

K. N. Sridharan·N. Shravan Kumar
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Abstract

Let $G$ be a locally compact second countable groupoid with a fixed Haar system $λ=\{λ^{u}\}_{u\in G^{0}}$ and $(Φ,Ψ)$ be a complementary pair of $N$-functions satisfying $Δ_{2}$-condition. In this article, we introduce the continuous field of Orlicz space $(L^Φ_{0},Δ_{1})$ and provide a sufficient condition for the space of continuous sections vanishing at infinity, denoted $E^Φ_{0}$, to be an Banach algebra under a suitable convolution. Further, the condition for a closed $C_{b}(G^{0})$-submodule $I$ of $E^Φ_{0}$ to be a left ideal is established. Moreover, we provide a groupoid analogue of the characterization of the space of convolutors of Morse-Transue space for locally compact groups.

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K. N. Sridharan, N. Shravan Kumar. 2026-07-26. Continuous field of Orlicz space on locally compact groupoids and related results. https://arxiv.org/abs/2501.05895

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