Real Analysis Exchange

On the Besicovitch Property for Parabolic Balls

Hugo Aimar and Liliana Forzani

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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

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

First available in Project Euclid: 6 June 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Besicovitch covering lemma real variable theory


Aimar, Hugo; Forzani, Liliana. On the Besicovitch Property for Parabolic Balls. Real Anal. Exchange 27 (2001), no. 1, 261--268.

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  • A. Calderón, Oral communication. Universidad de Buenos Aires, 1982.
  • M. Fuhrman, Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces. Studia Math. 115(1) (1995).
  • E. Sawyer and R. Wheeden, Weighted inequalities for fractional integrals on Euclidean and homogeneous space, Amer. J. Math. 114(2), (1992), 813–874.
  • E.Stein, and S. Wainger, Problems in harmonic analysis related to curvature. Bull. Amer. Math. Soc. 84(6) (1978), 1239–1295.