The Stein–Strömberg covering theorem in metric spaces
Copyright policy )The Stein–Strömberg covering theorem in metric spaces
In \cite{NaTa} Naor and Tao extended to the metric setting the $O(d \log d)$ bounds given by Stein and Strömberg for Lebesgue measure in $\mathbb{R}^d$, deriving these bounds first from a localization result, and second, from a random Vitali lemma. Here we show that the Stein-Strömberg original argument can also be adapted to the metric setting, giving a third proof. We also weaken the hypotheses, and additionally, we sharpen the estimates for Lebesgue measure.
15 pp, minor corrections, To appear J. Math. An. Appl
covering theorem, Maximal functions, Littlewood-Paley theory, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 42B25, maximal functions
covering theorem, Maximal functions, Littlewood-Paley theory, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 42B25, maximal functions
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