Operator-free sparse domination

Journal article (2022)

Authors

Andrei K. Lerner Bar-Ilan University
E. Lorist University of Helsinki
Sheldy Ombrosi Universidad Nacional del Sur
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Published Date

2022

Language

English

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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.