an:02203021
Zbl 1094.42021
Korenovskij, A. A.
Riesz rising sun lemma for several variables and the John-Nirenberg inequality
EN
Math. Notes 77, No. 1, 48-60 (2005); translation from Mat. Zametki 77, No. 1, 53-66 (2005).
00117563
2005
j
42B25 42C20
rising sun lemma; function of bounded mean oscillation; equimeasurable rearrangement; stopping-time technique; BMO
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.