The Stein-Strömberg covering theorem in metric spaces

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• 作者：J.M. Aldaz ^{jesus.munarriz@uam.es jesus.munarriz@icmat.es}
• 关键词：Covering theorem ; Maximal functions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：449
• 期：2
• 页码：1741-1753
• 全文大小：379 K
• 卷排序：449

文摘

In [8] Naor and Tao extended to the metric setting the O(dlog⁡d)O(dlog⁡d) bounds given by Stein and Strömberg for Lebesgue measure in RdRd, 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.