Convergence of ergodic-martingale paraproducts

Mario Stip\v{c}i\'c; Vjekoslav Kova\v{c}

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Convergence of ergodic-martingale paraproducts

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arxiv 2003.03651 v2 pith:MGMIK53A submitted 2020-03-07 math.PR math.CAmath.DS

Convergence of ergodic-martingale paraproducts

Vjekoslav Kova\v{c} , Mario Stip\v{c}i\'c This is my paper

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keywords convergenceaveragesergodicproblembackwardbilinearcommutingconjecture

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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.

Convergence of ergodic-martingale paraproducts

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