Abstract
In this paper, we introduce martingale Morrey spaces with variable exponents defined on a probability space. The weak-type and strong-type estimates for the Doob maximal operator on these spaces are established. We also construct the atomic decompositions for variable Hardy-Morrey spaces. As an application of the atomic decompositions, martingale inequalities among different Hardy-Morrey spaces are obtained. Further, we investigate the boundedness of fractional integral operators on martingale Hardy-Morrey spaces.
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