Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 847-857

NEW WEAK MARTINGALE HARDY SPACES OF MUSIELAK–ORLICZ TYPE

Anming Yang

Fudan University, School of Mathematical Sciences
Shanghai 200433, P.R. China; amyang14 'at' fudan.edu.cn

Abstract. The main purpose of this paper is to introduce the weak Musielak–Orlicz martingale spaces and establish several weak atomic decompositions for them. With the help of weak atomic decompositions, a sufficient condition for sublinear operators defined on weak Musielak–Orlicz martingale spaces to be bounded is given. Using the sufficient condition, a series of martingale inequalities are obtained. These results are generalizations of the previous results of weak martingale Hardy spaces and weak martingale Orlicz–Hardy spaces.

2010 Mathematics Subject Classification: Primary 60G46; Secondary 60G42.

Key words: Musielak–Orlicz function, weak Musielak–Orlicz martingale space, atomic decomposition, martingale inequality.

Reference to this article: A. Yang: Ann. Acad. Sci. Fenn. Math. 42 (2017), 847-857.

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https://doi.org/10.5186/aasfm.2017.4249