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Jiao, Yong; Zhao, Tiantian; Zhou, Dejian

Variable martingale Hardy-Morrey spaces. (English) Zbl 1431.42043

J. Math. Anal. Appl. 484, No. 1, Article ID 123722, 26 p. (2020).
Summary: 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.

Cited in 6 Documents

MSC:

42B35 Function spaces arising in harmonic analysis
42B25 Maximal functions, Littlewood-Paley theory
60G46 Martingales and classical analysis
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords:

Morrey spaces; Doob’s maximal operator; atomic decomposition; block spaces; fractional integral
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References:

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