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Martingale transforms and fractional integrals on rearrangement-invariant martingale Hardy spaces. (English) Zbl 1474.60115

Summary: We establish an interpolation result for the rearrangement-invariant martingale Hardy spaces. By using this interpolation result, we extend the mapping properties of the martingale transforms and the fractional integrals on martingale function spaces. In particular, we obtain the mapping properties on the martingale Hardy-Orlicz spaces, the grand martingale Hardy spaces and the martingale Hardy-Lorentz-Karamata spaces.

MSC:

60G42 Martingales with discrete parameter
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.)
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
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