Uchiyama's lemma and the John-Nirenberg inequality

Abstract

Using integral formulas based on Green's theorem and in particular a lemma of Uchiyama, we give simple proofs of comparisons of different BMO norms without using the John-Nirenberg inequality while we also give a simple proof of the strong John-Nirenberg inequality. Along the way we prove the inclusions of BMOA in the dual of H^1 and BMO in the dual of real H^1.

arXiv comment13 pages

References in corpus (1)

• Bellman Function and the $H^1-BMO$ Duality

Cited by in corpus (1)

• The John--Nirenberg constant of ${\mathrm{BMO}}^p,$ $1\le p\le 2$