Characterization of rearrangement invariant spaces with fixed points for the Hardy-Littlewood maximal operator

2004/09/01 by Joaquim Martin, Javier Soria, Martin, Joaquim +1
Mathematics · #42B25 #46E30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.FA #msc:42B25 #msc:46E30

paper · pdf · doi:10.48550/arxiv.math/0409017

8 pages

arxiv created 2004/09/01 · arxiv updated 2009/12/01

Abstract

We characterize the rearrangement invariant spaces for which there exists a non-constant fixed point, for the Hardy-Littlewood maximal operator (the case for the spaces L^p(ℝⁿ) was first considered by Korry in \citeKo). The main result that we prove is that the space L^{(n)/(n-2),∞}(ℝⁿ)∩ L^∞(ℝⁿ) is minimal among those having this property

Related

• Maximal operators on Lorentz spaces in non-doubling setting
• Fixed points of the uncentered Hardy-Littlewood maximal operator
• A boundedness criterion for the maximal operator on variable Lebesgue spaces
• Characterization of the restricted type spaces R(X)
• Hardy-Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type