A sharp estimate for the Hardy-Littlewood maximal function
Volume 134 / 1999
Studia Mathematica 134 (1999), 57-67
DOI: 10.4064/sm-134-1-57-67
Abstract
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.
