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Orlicz-Lorentz Hardy martingale spaces. (English) Zbl 1462.60055

Summary: Martingale Hardy spaces are widely studied in the field of mathematical physics and probability. In this paper, we develop the theory of Orlicz-Lorentz Hardy martingale spaces, which are much more wider than the classical Lorentz Hardy martingale spaces. More precisely, we first investigate several basic properties of Orlicz-Lorentz spaces, and then construct the atomic decomposition theorems of these martingale function spaces. Also, we establish the dual theorem of Orlicz-Lorentz Hardy spaces for martingales. Furthermore, we study the boundedness of generalized fractional integral operators \(I_\phi\) in this new framework, where \(\varphi\) is a non-negative concave function. The results partially extend the very recent results Y. Jiao et al. [Trans. Am. Math. Soc. 369, No. 1, 537–553 (2017; Zbl 1353.60043)].

MSC:

60G46 Martingales and classical analysis
60G42 Martingales with discrete parameter
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Citations:

Zbl 1353.60043
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References:

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