Causal sparse domination of Beurling maximal regularity operators

Journal article, 2023

We prove boundedness of Calderön–Zygmund operators acting in Banach function spaces on domains, defined by the L 1 Carleson functional and Lq (1 < q < ∞) Whitney averages. For such bounds to hold, we assume that the operator maps towards the boundary of the domain. We obtain the Carleson estimates by proving a pointwise domination of the operator, by sparse operators with a causal structure. The work is motivated by maximal regularity estimates for elliptic PDEs and is related to one-sided weighted estimates for singular integrals.