Oscillation and variation for singular integrals in higher dimensions

Campbell, James; Jones, Roger; Reinhold, Karin; Wierdl, Máté

doi:10.1090/S0002-9947-02-03189-6

Oscillation and variation for singular integrals in higher dimensions
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by James T. Campbell, Roger L. Jones, Karin Reinhold and Máté Wierdl PDF

Trans. Amer. Math. Soc. 355 (2003), 2115-2137 Request permission

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 $d \geq 1$. Our estimates give quantitative information on the speed of convergence of truncations of a singular integral operator, including upcrossing and $\lambda$ jump inequalities.

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