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

Convex body domination for a class of multi-scale operators