The best constant for centered Hardy-Littlewood maximal inequality

2003/11/25 by Antonios D. Melas · 2 citations
Mathematics · #math.CA

paper · pdf

published as Ann. of Math. (2), Vol. 157 (2003), no. 2, 647--688 · 42 pages, published version

arxiv created 2003/11/25 · arxiv updated 2009/12/01

Abstract

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 12C²-22C+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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