MAXIMAL INEQUALITY FOR HIGH-DIMENSIONAL CUBES

Confluentes Mathematici

AUBRUN, GUILLAUME¹ 

[1] Université de Lyon, CNRS, Institut Camille Jordan, France

关键词: Maximal inequality;    high-dimensional cubes;    Brownian bridge;   

DOI  :  10.1142/S1793744209000067

学科分类：数学（综合）

来源: World Scientific Publishing Co. Pte. Ltd.

【 摘 要 】

We present lower estimates for the best constant appearing in the weak (1, 1) maximal inequality in the space (Rn, ‖ · ‖∞). We show that this constant grows to infinity faster than (log n)1-o(1) when n tends to infinity. To this end, we follow and simplify the approach used by J. M. Aldaz. The new part of the argument relies on Donsker's theorem identifying the Brownian bridge as the limit object describing the statistical distribution of the coordinates of a point randomly chosen in the unit cube [0, 1]n (n large).

【 授权许可】

Unknown