A sharp estimate for the Hardy-Littlewood maximal function
L. Grafakos, Stephen J. Montgomery-Smith, O. Motrunich
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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