Operator-free sparse domination

Andrei K. Lerner, Emiel Lorist, Sheldy Ombrosi

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8 Scopus citations

Abstract

We obtain a sparse domination principle for an arbitrary family of functions Formula Presented, where Formula Presented and Q is a cube in Formula Presented. When applied to operators, this result recovers our recent works [37, 39]. On the other hand, our sparse domination principle can be also applied to non-operator objects. In particular, we show applications to generalised Poincaré-Sobolev inequalities, tent spaces and general dyadic sums. Moreover, the flexibility of our result allows us to treat operators that are not localisable in the sense of [39], as we will demonstrate in an application to vector-valued square functions.

Original languageEnglish
JournalForum of Mathematics, Sigma
Volume10
DOIs
StatePublished - 28 Feb 2022

Bibliographical note

Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press

Funding

The second author was supported by the Academy of Finland through Grant No. 336323. The third author was partially supported by ANPCyT PICT 2018-2501.

FundersFunder number
Academy of Finland336323
Agencia Nacional de Promoción Científica y TecnológicaPICT 2018-2501

    Keywords

    • 42B20
    • 42B25

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