1Dipartimento di Matematica Università di Milano - Bicocca 20125 Milano, Italy 2Departamento de Matemáticas y Computación Universidad de La Rioja 26004 Logroño, La Rioja, Spain
Colloquium Mathematicum, Tome 118 (2010) no. 2, pp. 379-389
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.
1
Dipartimento di Matematica Università di Milano - Bicocca 20125 Milano, Italy
2
Departamento de Matemáticas y Computación Universidad de La Rioja 26004 Logroño, La Rioja, Spain
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title = {Eigenfunctions of the {Hardy{\textendash}Littlewood
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Leonardo Colzani; Javier Pérez Lázaro. Eigenfunctions of the Hardy–Littlewood
maximal operator. Colloquium Mathematicum, Tome 118 (2010) no. 2, pp. 379-389. doi: 10.4064/cm118-2-2
