Geodesic
Abstract framework for John-Nirenberg inequalities and applications to Hardy spaces
Bernico, Frédéric1 ; Zhao, Jiman2
1 CNRS - Université de Nantes Laboratoire Jean Leray 2, rue de la Houssinière 44322 Nantes, France
2 School of Mathematical Sciences Beijing Normal University Key Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875, P.R. China
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 3, pp. 475-501

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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 [6], 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.

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Classification : 42B20, 46E30

Bernico, Frédéric 1 ; Zhao, Jiman 2

1 CNRS - Université de Nantes Laboratoire Jean Leray 2, rue de la Houssinière 44322 Nantes, France
2 School of Mathematical Sciences Beijing Normal University Key Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875, P.R. China 
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     title = {Abstract framework for {John-Nirenberg} inequalities and applications to {Hardy} spaces},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 11},
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Bernico, Frédéric; Zhao, Jiman. Abstract framework for John-Nirenberg inequalities and applications to Hardy spaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 3, pp. 475-501. http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_3_475_0/