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

• 论文 • 上一篇    下一篇

A FOUR-WEIGHT WEAK TYPE MAXIMAL INEQUALITY FOR MARTINGALES

任颜波   

  1. 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   

  1. 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: 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 = (fn)n≥0 with some constant C > 0, where Φ1, Φ2 are Young functions, wi (i = 1, 2, 3, 4) are weights, and f = fn 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 = (fn)n≥0 with some constant C > 0, where Φ1, Φ2 are Young functions, wi (i = 1, 2, 3, 4) are weights, and f = fn 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