engleski

Convergence of ergodic-martingale paraproducts

In this note we introduce a sequence of bilinear operators that unify ergodic averages and backward martingales in a nontrivial way. We establish its convergence in a range of L^p-norms and leave its a.s. convergence as an open problem. This problem shares some similarities with a well-known unresolved conjecture on a.s. convergence of double ergodic averages with respect to two commuting transformations.

Martingale ; Ergodic average ; Norm convergence ; Bilinear operator

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