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arXiv · 2602.21823

Compactness of averaging operators on non-reflexive Lebesgue spaces

Katsuhisa Koshino
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Abstract

Let $X$ be a Borel and Borel-regular metric measure space whose closed balls are of positive and finite measure. In this paper, we shall give equivalent conditions for averaging operators on non-reflexive Lebesgue spaces $L^1(X)$ and $L^\infty(X)$ on X to be compact, where X has some doubling property and satisfies certain uniform continuity between metric and measure.

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Katsuhisa Koshino. 2026-02-25. Compactness of averaging operators on non-reflexive Lebesgue spaces. https://arxiv.org/abs/2602.21823

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