Eigenfunctions of the Hardy–Littlewood maximal operator
Volume 118 / 2010
Colloquium Mathematicum 118 (2010), 379-389
MSC: Primary 42B25.
DOI: 10.4064/cm118-2-2
Abstract
We prove that peak shaped eigenfunctions of the one-dimensional uncentered Hardy–Littlewood maximal operator are symmetric and homogeneous. This implies that the norms of the maximal operator on $L(p)$ spaces are not attained.
