The best constant for the centered Hardy-Littlewood maximal inequality
成果类型：
Article
署名作者：
Melas, AD
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2003.157.647
发表日期：
2003
页码：
647-688
关键词：
摘要：
We find the exact value of the best possible constant C for the weak-type (1, 1) inequality for the one-dimensional centered Hardy-Littlewood maximal operator. We prove that C is the largest root of the quadratic equation 12C(2) - 22C + 5 = 0 thus obtaining C = 1.5675208.... This is the first time the best constant for one of the fundamental inequalities satisfied by a centered maximal operator is precisely evaluated.