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A sharp estimate for the Hardy-Littlewood maximal function

Loukas Grafakos; Stephen Montgomery-Smith; Olexei Motrunich — 1999

Studia Mathematica

The best constant in the usual $L^{p}$ norm inequality for the centered Hardy-Littlewood maximal function on $ℝ^{1}$ is obtained for the class of all “peak-shaped” functions. A function on the line is called peak-shaped if it is positive and convex except at one point. The techniques we use include variational methods.

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