Oscillation and variation for singular integrals in higher dimensions

Authors

James T. Campbell, University of MemphisFollow
Roger L. Jones, DePaul University
Karin Reinhold, State University of New York Albany
Máté Wierdl, University of Memphis

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. Our estimates give quantitative information on the speed of convergence of truncations of a singular integral operator, including upcrossing and λ jump inequalities.

Publication Title

Transactions of the American Mathematical Society

Recommended Citation

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