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arXiv · 1902.11080

A characterization of the uniform strong type $(1,1)$ bounds for averaging operators

J. M. Aldaz
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Abstract

We prove that in a metric measure space $(X, d, \mu)$, the averaging operators $A_{r, \mu }$ satisfy a uniform strong type $(1,1)$ bound $\sup_{r, \mu} \|A_{r, \mu }\|_{L^1\to L^1} < \infty$ if and only if $X$ satisfies a certain geometric condition, the equal radius Besicovitch intersection property.

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J. M. Aldaz. 2019-02-28. A characterization of the uniform strong type $(1,1)$ bounds for averaging operators. https://arxiv.org/abs/1902.11080

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