A FOUR-WEIGHT WEAK TYPE MAXIMAL INEQUALITY FOR MARTINGALES

doi:10.1007/s10473-019-0207-5

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (2): 413-419.doi: 10.1007/s10473-019-0207-5

A FOUR-WEIGHT WEAK TYPE MAXIMAL INEQUALITY FOR MARTINGALES

任颜波

School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China

收稿日期:2018-03-16 修回日期:2018-06-11 出版日期:2019-04-25 发布日期:2019-05-06
作者简介:Yanbo REN,ryb7945@sina.com
基金资助:
Supported by the National Natural Science Foundation of China (11871195).

A FOUR-WEIGHT WEAK TYPE MAXIMAL INEQUALITY FOR MARTINGALES

Yanbo REN

School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China

Received:2018-03-16 Revised:2018-06-11 Online:2019-04-25 Published:2019-05-06
Supported by:
Supported by the National Natural Science Foundation of China (11871195).

摘要/Abstract

摘要： In this article, some necessary and sufficient conditions are shown in order that weighted inequality of the form

holds a.e. for uniformly integrable martingales f = (f_n)n≥0 with some constant C > 0, where Φ₁, Φ₂ are Young functions, w_i (i = 1, 2, 3, 4) are weights, and f_∞ = f_n a.e. As an application, two-weight weak type maximal inequalities of martingales are considered, and particularly a new equivalence condition is presented.

关键词: weight, weak type inequality, martingale maximal operator, Young function

Abstract: In this article, some necessary and sufficient conditions are shown in order that weighted inequality of the form

holds a.e. for uniformly integrable martingales f = (f_n)n≥0 with some constant C > 0, where Φ₁, Φ₂ are Young functions, w_i (i = 1, 2, 3, 4) are weights, and f_∞ = f_n a.e. As an application, two-weight weak type maximal inequalities of martingales are considered, and particularly a new equivalence condition is presented.

Key words: weight, weak type inequality, martingale maximal operator, Young function

任颜波. A FOUR-WEIGHT WEAK TYPE MAXIMAL INEQUALITY FOR MARTINGALES[J]. 数学物理学报(英文版), 2019, 39(2): 413-419.

Yanbo REN. A FOUR-WEIGHT WEAK TYPE MAXIMAL INEQUALITY FOR MARTINGALES[J]. Acta mathematica scientia,Series B, 2019, 39(2): 413-419.

参考文献

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A FOUR-WEIGHT WEAK TYPE MAXIMAL INEQUALITY FOR MARTINGALES

A FOUR-WEIGHT WEAK TYPE MAXIMAL INEQUALITY FOR MARTINGALES

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