Doob’s inequality, Burkholder-Gundy inequality and martingale transforms on martingale Morrey spaces. (English) Zbl 1399.46038
Summary: We introduce the martingale Morrey spaces built on Banach function spaces. We establish Doob’s inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob’s inequality on martingale block spaces, we obtain the Davis’ decompositions for martingale Morrey spaces.
MSC:
| 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.) |
| 60G42 | Martingales with discrete parameter |
| 60G46 | Martingales and classical analysis |
Keywords:
Morrey spaces; Banach function space; block spaces; Doob’s inequality; Burkholder-Gundy inequality; martingale transform; Davis’ decomposition; martingaleReferences:
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