Rocky Mountain Journal of Mathematics

The Besicovitch covering lemma and maximal functions

Steven G. Krantz

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

Permanent link to this document
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

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

Keywords
Besicovitch covering lemma differentiation of integrals Fatou theorems

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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