Martingale Hardy spaces with variable exponents

By Yong Jiao, Dejian Zhou, Zhiwei Hao, Wei Chen. 2014

61 citations recorded by the source corpus.

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-Holder continuity condition in $\mathbb {R}^n.$

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9c098becdfdcca02fc52b363d8c566fbe8832a02

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In Applied Mathematics

1. Ferenc Weisz
2. Dachun Yang
3. Yong Jiao
4. Guangheng Xie
5. Wen Yuan
6. Yuan Zhou
7. Jun Liu
8. Luong Dang Ky

In Mathematical Physics

1. Ferenc Weisz
2. Guangheng Xie
3. Dachun Yang
4. Yong Jiao
5. Wen Yuan
6. Yuan Zhou
7. Jun Liu
8. Luong Dang Ky

Citations in the corpus

• New martingale inequalities and applications to Fourier analysis (2018, background): “The above five martingale Hardy spaces include weighted martingale Hardy spaces, martingale Orlicz–Hardy spaces in [52], weighted martingale Orlicz–Hardy spaces, and variable martingale Hardy spaces in [38, 40] as special cases (see also Remark 2.”