Some remarks on convex body domination

Convex body domination is an important elaboration of the technique of sparse domination that has seen significant development and applications over the past ten years. In this paper, we present an abstract framework for convex body domination, which also applies to Banach space -valued functions, and yields matrix-weighted norm inequalities in this setting. We explore applications to “generalised commutators”, obtaining new examples of bounded operators among linear combinations of compositions of pointwise multipliers and a singular integral operator.