English

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 CC for the weak type (1,1)(1,1) inequality for the one dimensional centered Hardy-Littlewood maximal operator. We prove that CC is the largest root of the quadratic equation 12C222C+5=012C^{2}-22C+5=0 thus obtaining C=1.5675208...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.

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