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Martingale transforms between Hardy-Orlicz spaces of $$L^\Phi$$ predictable martingales. (Chinese. English summary) Zbl 1274.46067
Summary: Using the technique of martingale transforms, the relation between Hardy-Orlicz spaces $$L^\Phi$$ of predictable martingales is investigated. Let $$\Phi_1$$ and $$\Phi_2$$ be two Young functions and $$\Phi_1\preccurlyeq^c\Phi_2$$ in some sense. We obtain a constructive proof that the elements in the Hardy-Orlicz space $$\mathcal{D}_{\Phi_1}$$ are exactly the martingale transforms of those in the Hardy-Orlicz space $$\mathcal{D}_{\Phi_2}$$.
##### MSC:
 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 60G48 Generalizations of martingales
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