鞅Orlicz-Lorentz-Karamata Hardy空间的实插值

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2025-06-20 DOI:10.1016/j.bulsci.2025.103690

Zhiwei Hao , Libo Li , Ferenc Weisz

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引用次数: 0

摘要

我们引入了一类新的Orlicz-Lorentz-Karamata空间，并在此框架下发展了鞅理论。更确切地说，我们研究了Orlicz-Lorentz-Karamata空间以及相应的鞅Hardy空间的实插值理论。结果证明了Doob极大不等式的推广。此外，还建立了鞅Hardy Orlicz-Lorentz-Karamata空间的原子分解。利用原子分解，给出了鞅Hardy Orlicz-Lorentz-Karamata空间的对偶性和广义John-Nirenberg定理。

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Real interpolation for martingale Orlicz-Lorentz-Karamata Hardy spaces

We introduce a new class of Orlicz-Lorentz-Karamata spaces and develop the martingale theory in this framework. More precisely, we study the real interpolation theory for Orlicz-Lorentz-Karamata spaces as well as for the corresponding martingale Hardy spaces. As a consequence, the generalization of Doob's maximal inequality will be proved. Moreover, the atomic decompositions of the martingale Hardy Orlicz-Lorentz-Karamata spaces are also established. With the help of atomic decompositions, the duality and generalized John-Nirenberg theorem for martingale Hardy Orlicz-Lorentz-Karamata spaces are presented.

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