Sparse domination for the lattice Hardy–Littlewood maximal operator

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 03 Oct 2018Embargo end date: 01 Jan 2017 Netherlands, Finland English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 147, pages 271-284 (issn: 0002-9939, eissn: 1088-6826,

Copyright policy )Funded by:AKA | Dyadic harmonic analysis ..., NWO | Harmonic Analysis for Sto...

Authors: Hänninen, Timo S. (author); Lorist, E. (author);

doi: 10.1090/proc/14236 , 10.48550/arxiv.1712.02592

arXiv: 1712.02592

handle: 10138/307057

Sparse domination for the lattice Hardy–Littlewood maximal operator

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Abstract

We study the domination of the lattice Hardy--Littlewood maximal operator by sparse operators in the setting of general Banach lattices. We prove that the admissible exponents of the dominating sparse operator are determined by the $q$-convexity of the Banach lattice.

14 pages, improved presentation

Countries

Netherlands, Finland

Related Organizations

University of Helsinki
Finland
Delft University of Technology
Netherlands

Keywords

BANACH-LATTICES, Maximal functions, Littlewood-Paley theory, POINTWISE ESTIMATE, Sparse domination, OSCILLATION DECOMPOSITION, 42B25 (Primary) 46E30, 46B42 (Secondary), Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Hardy-Littlewood maximal operator, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Banach lattices, Muckenhoupt weightsx, CALDERON-ZYGMUND OPERATORS, Banach lattice, $p$-convexity, $H^p$-spaces, sparse domination, SINGULAR-INTEGRALS, Muckenhoupt weights, Mathematics - Classical Analysis and ODEs, p-convexity, PROPERTY, Mathematics

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