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arXiv · 2003.03651

Convergence of ergodic-martingale paraproducts

Vjekoslav Kovač·Mario Stipčić
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Abstract

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.

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Vjekoslav Kovač, Mario Stipčić. 2020-03-07. Convergence of ergodic-martingale paraproducts. https://doi.org/10.1016/j.spl.2020.108826

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