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A sharp estimate for the Hardy-Littlewood maximal function

L. Grafakos·Stephen J. Montgomery-Smith·O. Motrunich
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Abstract

The best constant in the usual Lp norm inequality for the centered Hardy-Littlewood maximal function on R1 is obtained for the class of all ``peak-shaped'' functions. A positive function on the line is called ``peak-shaped'' if it is positive and convex except at one point. The techniques we use include convexity and an adaptation of the standard Euler-Langrange variational method.

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L. Grafakos, Stephen J. Montgomery-Smith, O. Motrunich. 1999-12-03. A sharp estimate for the Hardy-Littlewood maximal function. https://arxiv.org/abs/math/9704211

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