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.File in questo prodotto:
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