Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (2): 413-419.doi: 10.1007/s10473-019-0207-5

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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).

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

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