Geodesic
The best constant for centered Hardy-Littlewood maximal inequality
Antonios D. Melas1
1 Department of Mathematics, University of Athens, Athens, Greece
Annals of mathematics, Tome 157 (2003) no. 2, pp. 647-688.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 $C=1.5675208\ldots\,$ . This is the first time the best constant for one of the fundamental inequalities satisfied by a centered maximal operator is precisely evaluated.
DOI : 10.4007/annals.2003.157.647

Antonios D. Melas 1

1 Department of Mathematics, University of Athens, Athens, Greece 
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Antonios D. Melas. The best constant for centered Hardy-Littlewood maximal inequality. Annals of mathematics, Tome 157 (2003) no. 2, pp. 647-688. doi : 10.4007/annals.2003.157.647. http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.647/

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