Operator-free sparse domination

Andrei K. Lerner, Emiel Lorist, Sheldy Ombrosi

Research output: Contribution to journalArticlepeer-review

6 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

Funding Information:
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.

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

Keywords

  • 42B20
  • 42B25

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