A Search for Best Constants in the Hardy-Littlewood Maximal Theorem期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A Search for Best Constants in the Hardy-Littlewood Maximal Theorem

Authors:	Ron Dror Suman Ganguli Robert S Strichartz

Institution:	(1) Mathematics Department, Rice University, Houston, Texas 77251, USA;(2) Mathematics Department, White Hall, Cornell University, Ithaca, NY 14853, USA

Abstract:	Let $Mf(x) = \sup(1/2r)\int^{x+r}_{x-r} \|f(t)\|dt$ be the centered maximal operator on the line. Through a numerical search procedure, we have conjectural best constants for the weak-type 1-1 estimate (3/2) and the L^p estimate (the constant B(p,1) such that $M(\|x\|^{-1/p}) = B(p,1)\|x\|^{-1/p}).$ We prove that these constants are lower bounds for the best constants and discuss the numerical evidence for the conjectures.

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