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Atomic decomposition of predictable martingale Hardy space with variable exponents

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Abstract

This paper is mainly devoted to establishing an atomic decomposition of a predictable martingale Hardy space with variable exponents defined on probability spaces. More precisely, let (Ω,F, ℙ) be a probability space and p(·): Ω →(0,∞) be a F-measurable function such that \(0 < {\inf _{x \in \Omega }}p(x) \leqslant {\sup _{x \in \Omega }}p(x) < \infty \). It is proved that a predictable martingale Hardy space P p (·) has an atomic decomposition by some key observations and new techniques. As an application, we obtain the boundedness of fractional integrals on the predictable martingale Hardy space with variable exponents when the stochastic basis is regular.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, 405 Xiaoxiang Middle Road, Yuelu Area, Changsha, Hunan Province, 410083, P.R. China

    Zhiwei Hao

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  1. Zhiwei Hao
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Correspondence to Zhiwei Hao.

Additional information

This work is partly supported by National Natural Science Foundation of China (Grant No. 11471337), Hunan Provincial Natural Science Foundation (Grant No. 14JJ1004).

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Hao, Z. Atomic decomposition of predictable martingale Hardy space with variable exponents. Czech Math J 65, 1033–1045 (2015). https://doi.org/10.1007/s10587-015-0226-x

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  • DOI: https://doi.org/10.1007/s10587-015-0226-x

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