遍历鞅仿积的收敛性
Convergence of ergodic-martingale paraproducts
摘要：
本文引入了一个双线性算子序列，它以非平凡的方式统一了遍历平均和后向鞅。我们建立了它在一系列$L^p$ -范数下的收敛性，并将它的a. s.收敛是一个开放的问题。这个问题与a.s.上一个著名的未解猜想有一些相似之处。关于两个交换变换的双遍历平均的收敛性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
