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 Pp(·) 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., Zhiwei Hao., and Obsahuje seznam literatury