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Riesz rising sun lemma for several variables and the John-Nirenberg inequality. (English. Russian original) Zbl 1094.42021
Math. Notes 77, No. 1, 48-60 (2005); translation from Mat. Zametki 77, No. 1, 53-66 (2005).
Summary: 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.

##### MSC:
 42B25 Maximal functions, Littlewood-Paley theory 42C20 Other transformations of harmonic type
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##### References:
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