The best constant for centered Hardy-Littlewood maximal inequality

Details The best constant for centered Hardy-Littlewood maximal inequality The best constant for centered Hardy-Littlewood maximal inequality

2003-11-25

arxiv.org/abs/math/0311452v1

Ann. of Math. (2), Vol. 157 (2003), no. 2, 647--688

Mathematics

Classical Analysis and ODEs

42 pages, published version

Scientific paper

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.

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