The weak type (1,1) bounds for the maximal function associated to cubes grow to infinity with the dimension

被引：24

作者：

Aldaz, J. M. ^{[1
]}

机构：

[1] Univ Autonoma Madrid, Madrid, Spain

来源：

ANNALS OF MATHEMATICS | 2011年 / 173卷 / 02期

关键词：

CONVEX-BODIES; RN;

D O I：

10.4007/annals.2011.173.2.10

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M-d be the centered Hardy-Littlewood maximal function associated to cubes in R-d with Lebesgue measure, and let c(d) denote the lowest constant appearing in the weak type (1, 1) inequality satisfied by M-d. We show that c(d)->infinity as d ->infinity, thus answering, for the case of cubes, a longstanding open question of E. M. Stein and J. O. Stromberg.

引用

页码：1013 / 1023

页数：11