Eigenfunctions of the Hardy–Littlewood maximal operator

Volume 118 / 2010

Leonardo Colzani, Javier Pérez Lázaro Colloquium Mathematicum 118 (2010), 379-389 MSC: Primary 42B25. DOI: 10.4064/cm118-2-2


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.


  • Leonardo ColzaniDipartimento di Matematica
    Università di Milano - Bicocca
    20125 Milano, Italy
  • Javier Pérez LázaroDepartamento de Matemáticas y Computación
    Universidad de La Rioja
    26004 Logroño, La Rioja, Spain

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