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

• 成果类型: Article
• 署名作者: Aldaz, J. M.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.173.2.10
• 发表日期: 2011
• 页码: 1013-1023
• 关键词: convex-bodies; rn

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.