Uniform sparse domination of singular integrals via dyadic shifts

Using the Calderon-Zygmund decomposition, we give a novel and simple proof that L-2 bounded dyadic shifts admit a domination by positive sparse forms with linear growth in the complexity of the shift. Our estimate, coupled with Hytonen's dyadic representation theorem, upgrades to a positive sparse domination of the class u of singular integrals satisfying the assumptions of the classical T(l)-theorem of David and Journe. Furthermore, our proof extends rather easily to the R-n-valued case, yielding as a corollary the operator norm bound on the matrix weighted space L-2(TD;R-n) ([Graphic]) uniformly over T gM, which is the currently best known dependence.