Oscillation and Variation for Singular Integrals in Higher Dimensions

  title={Oscillation and Variation for Singular Integrals in Higher Dimensions},
  author={James T. P. Campbell and Roger L. Jones and Karin Reinhold and M{\'a}t{\'e} Wierdl},
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. Our estimates give quantitative information on the speed of convergence of truncations of a singular integral operator, including upcrossing and λ jump inequalities. 

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