Year: 2026
Type: preprint
Abstract: We prove that sparse domination of a bilinear form implies convex body domination. More precisely, if a bilinear form admits an $(r,s)$-sparse bound, then its coordinate-wise extension to $\mathbb C^n$-valued functions admits an $(r,s)$-convex body sparse bound. The proof relies on a randomization argument. We establish the result both for sparse families in a fixed dyadic lattice and for sparse families of arbitrary cubes. As an application, we deduce sparse domination for iterated commutators, with the local oscillations of the symbol appearing in the sparse form.
Source: arXiv (Cornell University)
Authors: Laukkarinen, Aapo, Lorist, Emiel
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204226022
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