Weak Orlicz-Hardy Martingale Spaces

2013/04/14 by Yong Jiao, Jiao, Yong, Lian Wu +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Primary 60G46 #Probability (math.PR) #Secondary 60G42 #math.FA #math.PR #msc:60G42 #msc:60G46

paper · pdf · doi:10.48550/arxiv.1304.3910

26 pages

arxiv created 2013/04/14 · arxiv updated 2013/04/16

Abstract

In this paper, several weak Orlicz-Hardy martingale spaces associated with concave functions are introduced, and some weak atomic decomposition theorems for them are established. With the help of weak atomic decompositions, a sufficient condition for a sublinear operator defined on the weak Orlicz-Hardy martingale spaces to be bounded is given. Further, we investigate the duality of weak Orlicz-Hardy martingale spaces and obtain a new John-Nirenberg type inequality when the stochastic basis is regular. These results can be regarded as weak versions of the Orlicz-Hardy martingale spaces due to Miyamoto, Nakai and Sadasue.

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