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Martingale Orlicz‐Hardy spaces
Author(s) -
Miyamoto Takashi,
Nakai Eiichi,
Sadasue Gaku
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201000109
Subject(s) - mathematics , martingale (probability theory) , doob's martingale inequality , hardy space , pure mathematics , martingale difference sequence , local martingale , birnbaum–orlicz space , mathematical analysis , interpolation space , functional analysis , biochemistry , chemistry , gene
The purpose of this paper is to introduce five martingale Orlicz‐Hardy spaces and to establish the atomic decomposition theorem. As applications we show the relation among five martingale Orlicz‐Hardy spaces and the duality, namely, the dual of martingale Orlicz‐Hardy spaces are generalized martingale Campanato spaces. Further, we prove a John‐Nirenberg type inequality for generalized martingale Campanato spaces when the stochastic basis is regular.