Eigenfunctions of the Hardy–Littlewood maximal operator

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2010 Italy English Publisher:Institute of Mathematics, Polish Academy of SciencesJournal:Colloquium Mathematicum, volume 118, pages 379-389 (issn: 0010-1354, eissn: 1730-6302,

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Authors: COLZANI, LEONARDO; Pérez Lázaro, J.;

doi: 10.4064/cm118-2-2

handle: 10281/28925

Eigenfunctions of the Hardy–Littlewood maximal operator

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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.

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Keywords

Hardy-Littlewood Maximal operator; Eigenfunctions; Operator Norm.

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