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Eigenfunctions of the Hardy-Littlewood maximal operator

Leonardo Colzani; Javier Pérez Lázaro — 2010

Colloquium Mathematicae

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.

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