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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Oscillation and variation for singular integrals in higher dimensions


Authors: James T. Campbell, Roger L. Jones, Karin Reinhold and Máté Wierdl
Journal: Trans. Amer. Math. Soc. 355 (2003), 2115-2137
MSC (2000): Primary 42B25; Secondary 40A30
Published electronically: November 14, 2002
MathSciNet review: 1953540
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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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Additional Information

James T. Campbell
Affiliation: Department of Mathematical Sciences, Dunn Hall 373, University of Memphis, Memphis, Tennessee 38152
Email: jtc@campbeljpc2.msci.memphis.edu

Roger L. Jones
Affiliation: Department of Mathematics, DePaul University, 2219 N. Kenmore, Chicago Illinois 60614
Email: rjones@condor.depaul.edu

Karin Reinhold
Affiliation: Department of Mathematics, University at Albany, SUNY, 1400 Washington Ave., Albany, New York 12222
Email: reinhold@csc.albany.edu

Máté Wierdl
Affiliation: Department of Mathematical Sciences, Dunn Hall 373, University of Memphis, Memphis, Tennessee 38152
Email: mw@moni.msci.memphis.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03189-6
PII: S 0002-9947(02)03189-6
Keywords: Singular integrals, square functions, variation, oscillation, upcrossing inequalities, jump inequalities
Received by editor(s): April 4, 2002
Received by editor(s) in revised form: August 19, 2002
Published electronically: November 14, 2002
Additional Notes: The second author was partially supported by NSF Grant DMS—9302012
The fourth author was partially supported by NSF Grant DMS—9500577
Article copyright: © Copyright 2002 American Mathematical Society