Real Analysis Exchange

On the Besicovitch Property for Parabolic Balls

Hugo Aimar and Liliana Forzani

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Abstract

Let $ p \ge 1 $ and $ a_1, \dots , a_n $ be positive given numbers. We prove that, the family of all solids of $ {\mathcal R}^n $ of the type $\sum_{i=1}^n \left( \frac{|{x_i}| }{ r^{a_i}} \right)^p < 1 $, $ r > 0 $ satisfies the Besicovitch covering lemma if and only if $ p \ge \frac{\max a_i }{\min a_i } $.

Article information

Source
Real Anal. Exchange, Volume 27, Number 1 (2001), 261-268.

Dates
First available in Project Euclid: 6 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1212763965

Mathematical Reviews number (MathSciNet)
MR1887856

Zentralblatt MATH identifier
1018.42008

Subjects
Primary: 42B99: None of the above, but in this section 26B99: None of the above, but in this section

Keywords
Besicovitch covering lemma real variable theory

Citation

Aimar, Hugo; Forzani, Liliana. On the Besicovitch Property for Parabolic Balls. Real Anal. Exchange 27 (2001), no. 1, 261--268. https://projecteuclid.org/euclid.rae/1212763965


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