Ergodic averages on circles
Copyright policy )Ergodic averages on circles
Let \(\sigma\) be a rotation invariant measure on \(S^1\), and let \(T_i\) \((i=1,2)\) be two commuting measure preserving flows on a probability space \((X,B,\mu)\). The author proves the following result (extending \textit{R. Jones} [J. Anal. Math. 61, 29-45 (1993; Zbl 0828.28007)]), that for \(p>2\) and \(f\in L^p(\mu)\) the averages \(\int_{S^1} f(T^{us}_1\circ T^{us}_2(x))\sigma(ds)\) converge a.e. to \(\int f d\mu\).
- Indiana University United States
- DePaul University United States
maximal variational inequality, commuting transformations, measure preserving flows, One-parameter continuous families of measure-preserving transformations, ergodic averages
maximal variational inequality, commuting transformations, measure preserving flows, One-parameter continuous families of measure-preserving transformations, ergodic averages
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