鞅极大算子的加权弱型不等式的统一形式

Pub Date : 2021-06-29 DOI:10.1556/012.2021.58.2.1495

Yanbo B. Ren, Congbian Ma

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引用次数: 0

摘要

设N和Φ1是定义在[0，∞)上的非递减非负函数，Φ2是N函数，u, v和w是权值。考虑了鞅极大算子f *的加权弱型不等式的一个统一形式，给出了其成立的若干必要条件和su@cient条件。此外，我们给出了鞅的三权弱型极大不等式的完整刻画。我们的结果推广了关于鞅极大算子加权理论的一些已知结果。

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A Unified Version of Weighted Weak Type Inequality for Martingale Maximal Operators

Let ɣ and Φ1 be nondecreasing and nonnegative functions defined on [0, ∞), and Φ2 is an N -function, u, v and w are weights. A unified version of weighted weak type inequality of the formfor martingale maximal operators f ∗ is considered, some necessary and su@cient conditions for it to hold are shown. In addition, we give a complete characterization of three-weight weak type maximal inequality of martingales. Our results generalize some known results on weighted theory of martingale maximal operators.

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