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.

Colzani, L., Pérez Lázaro, J. (2010). Eigenfunctions of the Hardy-Littlewood maximal operator. COLLOQUIUM MATHEMATICUM, 118(2), 379-389 [10.4064/cm118-2-2].

Eigenfunctions of the Hardy-Littlewood maximal operator

COLZANI, LEONARDO;
2010

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.
Articolo in rivista - Articolo scientifico
Hardy-Littlewood Maximal operator; Eigenfunctions; Operator Norm.
English
2010
118
2
379
389
none
Colzani, L., Pérez Lázaro, J. (2010). Eigenfunctions of the Hardy-Littlewood maximal operator. COLLOQUIUM MATHEMATICUM, 118(2), 379-389 [10.4064/cm118-2-2].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/28925
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