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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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