The best constant for centered Hardy-Littlewood maximal inequality
Classical Analysis and ODEs
2007-05-23 v1
Abstract
We find the exact value of the best possible constant for the weak type inequality for the one dimensional centered Hardy-Littlewood maximal operator. We prove that is the largest root of the quadratic equation thus obtaining . This is the first time the best constant for one of the fundamental inequalities satisfied by a centered maximal operator is precisely evaluated.
Cite
@article{arxiv.math/0311452,
title = {The best constant for centered Hardy-Littlewood maximal inequality},
author = {Antonios D. Melas},
journal= {arXiv preprint arXiv:math/0311452},
year = {2007}
}
Comments
42 pages, published version