Real Analysis Exchange

On the Discretization Technique for the Hardy-Littlewood Maximal Operators

Dariusz Kosz

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Abstract

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

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

Dates
First available in Project Euclid: 30 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.rae/1490839331

Mathematical Reviews number (MathSciNet)
MR3597320

Zentralblatt MATH identifier
06848929

Subjects
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.)

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

Citation

Kosz, Dariusz. On the Discretization Technique for the Hardy-Littlewood Maximal Operators. Real Anal. Exchange 41 (2016), no. 2, 287--292. https://projecteuclid.org/euclid.rae/1490839331


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