论文标题
具有通勤转换和成对依赖性多项式迭代的沿贡族平均值的静态控制
Seminorm control for ergodic averages with commuting transformations and pairwise dependent polynomial iterates
论文作者
论文摘要
我们检查了多项式迭代的通勤变换的多个沿贡族平均值，其中多项式可能是成对依赖的。特别是，我们表明，只要系统满足某些轻度的千古假设，这种平均值就由Gowers-host-Kra eminors控制。将这一结果与早期工作中建立的关节终对性的一般标准相结合，我们确定了这种平均值是共同呈现的必要条件，从某种意义上说，它们均匀地融入了积分的均值，或者是弱共同的ergodic，因为它们会融合到有条件预期的产物中。作为推论，我们推断出Donoso，Koutsogiannis和Sun的特殊案例，并以更强的形式推断出来。
We examine multiple ergodic averages of commuting transformations with polynomial iterates in which the polynomials may be pairwise dependent. In particular, we show that such averages are controlled by the Gowers-Host-Kra seminorms whenever the system satisfies some mild ergodicity assumptions. Combining this result with the general criteria for joint ergodicity established in our earlier work, we determine a necessary and sufficient condition under which such averages are jointly ergodic, in the sense that they converge in the mean to the product of integrals, or weakly jointly ergodic, in that they converge to the product of conditional expectations. As a corollary, we deduce a special case of a conjecture by Donoso, Koutsogiannis, and Sun in a stronger form.
