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October 2019 Atomic characterizations of weak martingale Musielak–Orlicz Hardy spaces and their applications
Guangheng Xie, Dachun Yang
Banach J. Math. Anal. 13(4): 884-917 (October 2019). DOI: 10.1215/17358787-2018-0050

Abstract

Let (Ω,F,P) be a probability space, and let φ:Ω×[0,)[0,) be a Musielak–Orlicz function. In this article, we establish the atomic characterizations of weak martingale Musielak–Orlicz Hardy spaces WHφs(Ω), WHφM(Ω), WHφS(Ω), WPφ(Ω), and WQφ(Ω). We then use these atomic characterizations to obtain the boundedness of σ-sublinear operators from weak martingale Musielak–Orlicz Hardy spaces to weak Musielak–Orlicz spaces, as well as some martingale inequalities which further clarify the relationships among these weak martingale Musielak–Orlicz Hardy spaces. All these results improve and generalize the corresponding results on weak martingale Orlicz–Hardy spaces. Moreover, we improve all the known results on weak martingale Musielak–Orlicz Hardy spaces. In particular, both the boundedness of σ-sublinear operators and the martingale inequalities, for weak weighted martingale Hardy spaces as well as for weak weighted martingale Orlicz–Hardy spaces, are new.

Citation

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Guangheng Xie. Dachun Yang. "Atomic characterizations of weak martingale Musielak–Orlicz Hardy spaces and their applications." Banach J. Math. Anal. 13 (4) 884 - 917, October 2019. https://doi.org/10.1215/17358787-2018-0050

Information

Received: 14 November 2018; Accepted: 20 December 2018; Published: October 2019
First available in Project Euclid: 9 October 2019

zbMATH: 07118767
MathSciNet: MR4016902
Digital Object Identifier: 10.1215/17358787-2018-0050

Subjects:
Primary: 60G42
Secondary: 42B25, 42B35, 60G46

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 4 • October 2019
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