On the centered Hardy-Littlewood maximal operator

Melas, Antonios

doi:10.1090/S0002-9947-02-02900-8

On the centered Hardy-Littlewood maximal operator
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by Antonios D. Melas PDF

Trans. Amer. Math. Soc. 354 (2002), 3263-3273 Request permission

Abstract:

We will study the centered Hardy-Littlewood maximal operator acting on positive linear combinations of Dirac deltas. We will use this to obtain improvements in both the lower and upper bounds or the best constant $C$ in the $L^{1}\rightarrow$ weak $L^{1}$ inequality for this operator. In fact we will show that $\frac {11+\sqrt {61}}{12}=1.5675208...\leq C\leq \frac {5} {3}=1.66...$.

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