A+ CATEGORY SCIENTIFIC UNIT

A sharp estimate for the Hardy-Littlewood maximal function

Volume 134 / 1999

Loukas Grafakos, Stephen Montgomery-Smith, Olexei Motrunich 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.

Authors

  • Loukas Grafakos
  • Stephen Montgomery-Smith
  • Olexei Motrunich

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