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arXiv · 1404.2395

Martingale Hardy spaces with variable exponents

Yong Jiao·Dejian Zhou·Zhiwei Hao·Wei Chen
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Abstract

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 get a $(1,p(\cdot),\infty)$-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 probabilistic characterization of $p(\cdot)$ to replace the so-called log-H\"{o}lder continuity condition in $\mathbb {R}^n.$

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Yong Jiao, Dejian Zhou, Zhiwei Hao, Wei Chen. 2014-04-09. Martingale Hardy spaces with variable exponents. https://doi.org/10.1215/17358787-3649326

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