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2019 The Besicovitch covering lemma and maximal functions
Steven G. Krantz
Rocky Mountain J. Math. 49(2): 539-555 (2019). DOI: 10.1216/RMJ-2019-49-2-539

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.

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Steven G. Krantz. "The Besicovitch covering lemma and maximal functions." Rocky Mountain J. Math. 49 (2) 539 - 555, 2019. https://doi.org/10.1216/RMJ-2019-49-2-539

Information

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

zbMATH: 07079983
MathSciNet: MR3973239
Digital Object Identifier: 10.1216/RMJ-2019-49-2-539

Subjects:
Primary: 42B25, 42B99

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 2 • 2019
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