Geodesic
JOP's counting function and Jones' square function
Karin Reinhold1
1 Department of Mathematics University at Albany, SUNY 1400 Washington Ave. Albany, NY 12222, U.S.A.
Studia Mathematica, Tome 172 (2006) no. 1, pp. 1-23 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study a class of square functions in a general framework with applications to a variety of situations: samples along subsequences, averages of $\mathbb Z_+^d$ actions and of positive $L^1$ contractions. We also study the relationship between a counting function first introduced by Jamison, Orey and Pruitt, in a variety of situations, and the corresponding ergodic averages. We show that the maximal counting function is not dominated by the square functions.
DOI : 10.4064/sm172-1-1
Keywords: study class square functions general framework applications variety situations samples along subsequences averages mathbb actions positive contractions study relationship between counting function first introduced jamison orey pruitt variety situations corresponding ergodic averages maximal counting function dominated square functions

Karin Reinhold 1

1 Department of Mathematics University at Albany, SUNY 1400 Washington Ave. Albany, NY 12222, U.S.A. 
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Karin Reinhold. JOP's counting function  and Jones' square function. Studia Mathematica, Tome 172 (2006) no. 1, pp. 1-23. doi: 10.4064/sm172-1-1

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