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Square functions in ergodic theory

Published online by Cambridge University Press:  19 September 2008

Roger L. Jones ,
Iosif V. Ostrovskii  and
Joseph M. Rosenblatt
Roger L. Jones
Affiliation:
Department of Mathematics, DePaul University, Chicago, IL 60614, USA
Iosif V. Ostrovskii
Affiliation:
Institute for Low Temperature, Physics and Engineering, 47 Lenin Avenue, Kharkov 310164, Ukraine
Joseph M. Rosenblatt
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA
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Abstract

Given the usual averages in ergodic theory, let n1 ≤ n2 ≤ … and . There is a strong inequality ‖Sf‖2 ≤ 25‖f‖2 and there is a weak inequality m{Sf > λ} ≤ (7000/λ)‖f‖1. Related results and questions for other variants of this square function are also discussed.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 2 , April 1996 , pp. 267 - 305
Copyright
Copyright © Cambridge University Press 1996

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References

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