Oscillation and variation for singular integrals in higher dimensions
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.
Transactions of the American Mathematical Society
Campbell, J., Jones, R., Reinhold, K., & Wierdl, M. (2003). Oscillation and variation for singular integrals in higher dimensions. Transactions of the American Mathematical Society, 355 (5), 2115-2137. https://doi.org/10.1090/S0002-9947-02-03189-6