Banach Journal of Mathematical Analysis

Martingale Hardy spaces with variable exponents

Yong Jiao, Dejian Zhou, Zhiwei Hao, and Wei Chen

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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.

Article information

Banach J. Math. Anal., Volume 10, Number 4 (2016), 750-770.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G46: Martingales and classical analysis
Secondary: 60G42: Martingales with discrete parameter

martingale Hardy spaces variable exponents atomic decomposition


Jiao, Yong; Zhou, Dejian; Hao, Zhiwei; Chen, Wei. Martingale Hardy spaces with variable exponents. Banach J. Math. Anal. 10 (2016), no. 4, 750--770. doi:10.1215/17358787-3649326.

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