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Oscillation inequalities for rectangles
Author(s):
Roger
L.
Jones;
Joseph
M.
Rosenblatt;
Máté
Wierdl
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1349-1358.
MSC (2000):
Primary 42B25, 28D05;
Secondary 40A30
Posted:
November 30, 2000
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Abstract:
In this paper we extend previously obtained results on  norm inequalities  for square functions, oscillation and variation operators, with  actions, to the case of  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.
References:
-
- 1.
- Bellow, A., Transfer principles in ergodic theory, in Harmonic Analysis and Partial Differential Equations, Chicago Lectures in Mathematics, M. Christ, C. Kenig and C. Sadosky ed., University of Chicago Press, Chicago 1999, pages 27-39.
- 2.
- Caledrón, A. P., Ergodic theory and translation invariant operators, Proc. Nat. Acad. of Sci., USA 59 (1968) 349-353. MR 37:2939
- 3.
- Fefferman, C. and Stein, E. M., Some maximal inequalities Amer. J. Math. 93 107-115. MR 44:2026
- 4.
- Jones, R. L., Ostrovskii, I. and Rosenblatt, J. Square functions in ergodic theory, Ergod. Th. & Dynam. Sys., 16 (1996) 267-305. MR 97f:28044
- 5.
- Jones R. L., Kaufman, R., Rosenblatt, J. and Wierdl, M. Oscillation in ergodic theory, Ergod. Th. & Dynam. Sys., 18 (1998) 889-935. MR 2000b:28019
- 6.
- Jones, R.L., Rosenblatt, J. and Wierdl, M., Oscillation inequalities, the higher dimensional case, preprint.
- 7.
- Jones, R.L., Rosenblatt, J. and Wierdl, M., Counting in ergodic theory, Canad. J. Math., 51 (1999) 996-1019. MR 2000i:28021
- 8.
- Kalikow, S. and Weiss, B., Fluctuations of ergodic averages, Il. J. Math., 43 (1999) 480-488. CMP 99:17
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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:
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
Posted:
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
Copyright of article:
Copyright
2000,
American Mathematical Society
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