A note on sharp 1-dimensional Poincare inequalities

被引：9

作者：

Chua, SK

Wheeden, RL

机构：

[1] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore

[2] Rutgers State Univ, Dept Math, New Brunswick, NJ 08903 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2006年 / 134卷 / 08期

关键词：

D O I：

10.1090/S0002-9939-06-08545-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let 1 < p < infinity and -infinity < a < b < infinity. We show by using elementary methods that the best constant C ( necessarily independent of a and b) for which the 1-dimensional Poincare inequality parallel to f - f(av)parallel to(1)(L)([a, b]) <= C(b - a)(2-1/p) parallel to f'parallel to L-P[a,L-b] holds for all Lipschitz continuous functions f, with f(av) = integral/(b-a), is C = 1/2(1+p')-1/p'.

引用

页码：2309 / 2316

页数：8

共 29 条

[21] GAUSSIAN KERNELS HAVE ONLY GAUSSIAN MAXIMIZERS [J].