Open Access
October 2016 Martingale Hardy spaces with variable exponents
Yong Jiao, Dejian Zhou, Zhiwei Hao, Wei Chen
Banach J. Math. Anal. 10(4): 750-770 (October 2016). DOI: 10.1215/17358787-3649326


In this paper, we introduce Hardy spaces with variable exponents defined on a probability space and develop the martingale theory of variable Hardy spaces. We prove the weak-type and strong-type inequalities on Doob’s maximal operator, and we get a (1,p(),)-atomic decomposition for Hardy martingale spaces associated with conditional square functions. As applications, we obtain a dual theorem and the John–Nirenberg inequalities in the frame of variable exponents. The key ingredient is that we find a condition with a probabilistic characterization of p() to replace the so-called log-Hölder continuity condition in Rn.


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Yong Jiao. Dejian Zhou. Zhiwei Hao. Wei Chen. "Martingale Hardy spaces with variable exponents." Banach J. Math. Anal. 10 (4) 750 - 770, October 2016.


Received: 7 October 2015; Accepted: 11 January 2016; Published: October 2016
First available in Project Euclid: 20 September 2016

zbMATH: 1354.42042
MathSciNet: MR3548624
Digital Object Identifier: 10.1215/17358787-3649326

Primary: 60G46
Secondary: 60G42

Keywords: atomic decomposition , martingale Hardy spaces , variable exponents

Rights: Copyright © 2016 Tusi Mathematical Research Group

Vol.10 • No. 4 • October 2016
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