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JOP's counting function and Jones' square function

Tom 172 / 2006

Karin Reinhold Studia Mathematica 172 (2006), 1-23 MSC: Primary 42B25; Secondary 40A30. DOI: 10.4064/sm172-1-1

Streszczenie

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.

Autorzy

  • Karin ReinholdDepartment of Mathematics
    University at Albany, SUNY
    1400 Washington Ave.
    Albany, NY 12222, U.S.A.
    e-mail

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