Geodesic
Atomic decomposition of predictable martingale Hardy space with variable exponents
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 4, pp. 1033-1045.

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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 $(\Omega , \mathcal {F}, \mathbb {P})$ be a probability space and $p(\cdot )\colon \Omega \rightarrow (0,\infty )$ be a $\mathcal {F}$-measurable function such that $0\inf \nolimits _{x\in \Omega }p(x)\leq \sup \nolimits _{x\in \Omega }p(x)\infty $. It is proved that a predictable martingale Hardy space $\mathcal P_{p(\cdot )}$ 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.
DOI : 10.1007/s10587-015-0226-x
Classification : 60G42, 60G46
Keywords: variable exponent; atomic decomposition; martingale Hardy space; fractional integral 
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     title = {Atomic decomposition of predictable martingale {Hardy} space with variable exponents},
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Hao, Zhiwei. Atomic decomposition of predictable martingale Hardy space with variable exponents. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 4, pp. 1033-1045. doi : 10.1007/s10587-015-0226-x. http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0226-x/

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