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Riesz rising sun lemma for several variables and the John-Nirenberg inequality

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Abstract

We obtain a multidimensional analog of the well-known Riesz rising sun lemma. We prove a more precise version of this lemma for space dimension d = 2 . We use these lemmas to establish an anisotropic analog of the John-Nirenberg inequality for functions of bounded mean oscillation with an exact constant in the exponent. Earlier, this exact constant was only known in the one-dimensional case.

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Authors and Affiliations

  1. Institute for Mathematics, Economics, and Mechanics, I. I. Mechnikov Odessa National University, Russia

    A. A. Korenovskii

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  1. A. A. Korenovskii
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Translated from Matematicheskie Zametki, vol. 77, no. 1, 2005, pp. 53–66.

Original Russian Text Copyright © 2005 by A. A. Korenovskii.

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Korenovskii, A.A. Riesz rising sun lemma for several variables and the John-Nirenberg inequality. Math Notes 77, 48–60 (2005). https://doi.org/10.1007/s11006-005-0005-3

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  • DOI: https://doi.org/10.1007/s11006-005-0005-3

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