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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Oscillation inequalities for rectangles


Authors: Roger L. Jones, Joseph M. Rosenblatt and Máté Wierdl
Journal: Proc. Amer. Math. Soc. 129 (2001), 1349-1358
MSC (2000): Primary 42B25, 28D05; Secondary 40A30
Published electronically: November 30, 2000
MathSciNet review: 1814160
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Abstract: In this paper we extend previously obtained results on $L^p$norm inequalities $(1<p<\infty)$ for square functions, oscillation and variation operators, with $\mathbb Z$ actions, to the case of $\mathbb Z^d$actions. The technique involves the use of a result about vector valued maximal functions, due to Fefferman and Stein, to reduce the problem to a situation where we can apply our previous results.


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Additional Information

Roger L. Jones
Affiliation: Department of Mathematics, DePaul University, 2320 N. Kenmore, Chicago, Illinois 60614
Email: rjones@condor.depaul.edu

Joseph M. Rosenblatt
Affiliation: Department of Mathematics, University of Illinois at Urbana, Urbana, Illinois 61801
Email: jrsnbltt@symcom.math.uiuc.edu

Máté Wierdl
Affiliation: Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee 38152
Email: wierdlm@mathsci.msci.memphis.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-06032-9
PII: S 0002-9939(00)06032-9
Keywords: Convergence of ergodic averages, square functions, variation, oscillation, upcrossing inequalities, jump inequalities
Received by editor(s): July 15, 1999
Published electronically: November 30, 2000
Additional Notes: The first author was partially supported by NSF Grant DMS—9531526
The second author was partially supported by NSF Grant DMS—9705228
The third author was partially supported by NSF Grant DMS—9500577
Communicated by: Michael Handel
Article copyright: © Copyright 2000 American Mathematical Society