Rocky Mountain Journal of Mathematics

The Besicovitch covering lemma and maximal functions

Steven G. Krantz

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This paper has two purposes. First, we explain and describe the Besicovitch covering lemma, and we provide a new proof. Applications are given, particularly to the ideas of Nagel and Stein about Fatou theorems through approach regions which are not nontangential. Second, we examine the strong maximal function and give a new, simple, geometric proof of its $L^p$ boundedness.

Article information

Rocky Mountain J. Math., Volume 49, Number 2 (2019), 539-555.

Received: 8 February 2018
Revised: 10 July 2018
First available in Project Euclid: 23 June 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B25: Maximal functions, Littlewood-Paley theory 42B99: None of the above, but in this section

Besicovitch covering lemma differentiation of integrals Fatou theorems


Krantz, Steven G. The Besicovitch covering lemma and maximal functions. Rocky Mountain J. Math. 49 (2019), no. 2, 539--555. doi:10.1216/RMJ-2019-49-2-539.

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