Ergodic Theory and Dynamical Systems

Research Article

Square functions in ergodic theory

Roger L. Jonesa1, Iosif V. Ostrovskiia2 and Joseph M. Rosenblatta3 p1

a1 Department of Mathematics, DePaul University, Chicago, IL 60614, USA

a2 Institute for Low Temperature, Physics and Engineering, 47 Lenin Avenue, Kharkov 310164, Ukraine

a3 Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA

Abstract

Given the usual averages in ergodic theory, let n1n2 ≤ … and . There is a strong inequality Sf2 ≤ 25f2 and there is a weak inequality m{Sf > λ} ≤ (7000/λ)f1. Related results and questions for other variants of this square function are also discussed.

(Received April 20 1994)

(Revised January 05 1995)

Correspondence

p1 Current address: Department of Mathematics, University of Illinois, Urbana, IL 61801, USA.

Footnotes

† Partially supported by NSF Grant DMS-9302012.

‡ Partially supported by NSF Grant DMS-9103056.