Abstract framework for John Nirenberg inequalities and applications to Hardy spaces

Frederic Bernicot (1) , Jiman Zhao (2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 SMS - School of Mathematical Sciences [Beijing]

In this paper, we develop an abstract framework for John-Nirenberg inequalities associated to BMO-type spaces. This work can be seen as the sequel of [5], where the authors introduced a very general framework for atomic and molecular Hardy spaces. Moreover, we show that our assumptions allow us to recover some already known John-Nirenberg inequalities. We give applications to the atomic Hardy spaces too.

Mots clés: BMO spaces; John-Nirenberg inequalities; Hardy spaces

Domaines: Analyse fonctionnelle [math.FA]

Frederic Bernicot, Jiman Zhao. Abstract framework for John Nirenberg inequalities and applications to Hardy spaces. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2012, 11 (3), pp.475-501. ⟨hal-00460699⟩