Oscillation and variation for singular integrals in higher dimensions

Abstract

In this paper we continue our investigations of square function inequalities in harmonic analysis. Here we investigate oscillation and variation inequalities for singular integral operators in dimensions d ≥ 1 d \geq 1 . Our estimates give quantitative information on the speed of convergence of truncations of a singular integral operator, including upcrossing and λ \lambda jump inequalities.