Convex body domination for a class of multi-scale operators

Abstract

The technique of sparse domination, i.e., dominating operators with sums of averages taken over sparsely distributed cubes, has seen rapid development recently within the realms of harmonic analysis. A useful extension of sparse domination called convex body domination allows one to estimate operators in matrix-weighted spaces. In this paper, we extend recent sparse domination results for a class of multi-scale operators due to Beltran, Roos and Seeger to the convex body setting and prove that this implies quantitative matrix-weighted norm bounds for these operators and their commutators.