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Duality theorem for B ‐valued martingale Orlicz–Hardy spaces associated with concave functions
Author(s) -
Yu Lin
Publication year - 2016
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.201400174
Subject(s) - mathematics , martingale (probability theory) , convexity , hardy space , banach space , pure mathematics , local martingale , smoothness , eberlein–šmulian theorem , mathematical analysis , discrete mathematics , lp space , financial economics , economics
The dual space of B ‐valued martingale Orlicz–Hardy spaceH Φ s ( p )( B )with a concave function Φ, which is associated with the conditional p ‐variation of B ‐valued martingale, is characterized. To obtain the results, a new type of Campanato spaces for B ‐valued martingales is introduced and the classical technique of atomic decompositions is improved. Some results obtained here are connected closely with the p ‐uniform smoothness and q ‐uniform convexity of the underlying Banach space.