Year: 2022
Type: article
Abstract: We obtain a sparse domination principle for an arbitrary family of functions $f(x,Q)$ , where $x\in {\mathbb R}^{n}$ andQis a cube in ${\mathbb R}^{n}$ . 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.
Source: Forum of Mathematics Sigma
DOI: 10.1017/fms.2022.8
Authors: Andrei K. Lerner, Emiel Lorist, Sheldy Ombrosi
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,500
Awards: G1749444191, G3244354378
OpenAlex ID: W3173372399