## Rocky Mountain Journal of Mathematics

### The Besicovitch covering lemma and maximal functions

Steven G. Krantz

#### Abstract

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

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

Dates
Revised: 10 July 2018
First available in Project Euclid: 23 June 2019

https://projecteuclid.org/euclid.rmjm/1561318392

Digital Object Identifier
doi:10.1216/RMJ-2019-49-2-539

Mathematical Reviews number (MathSciNet)
MR3973239

Zentralblatt MATH identifier
07079983

#### Citation

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. https://projecteuclid.org/euclid.rmjm/1561318392

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