Real Analysis Exchange

On the Discretization Technique for the Hardy-Littlewood Maximal Operators

Dariusz Kosz

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We extend the discretization method of de Guzmán to the setting of general metric measure spaces with mild assumptions on their structures. This method allows one to relate the best constants in the weak type $(1,1)$ inequalities for the relevant centered and uncentered Hardy-Littlewood maximal operators with the analogous constants received by applying the maximal operators to sums of Dirac deltas rather than to $L^1$ functions.

Article information

Real Anal. Exchange, Volume 41, Number 2 (2016), 287-292.

First available in Project Euclid: 30 March 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Hardy-Littlewood maximal operators discretization weak type $(1,1)$


Kosz, Dariusz. On the Discretization Technique for the Hardy-Littlewood Maximal Operators. Real Anal. Exchange 41 (2016), no. 2, 287--292.

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