论文标题
某些连续时双段平均值的侧面收敛
Pointwise convergence of certain continuous-time double ergodic averages
论文作者
论文摘要
我们证明了A.E.连续时间二次二次平均相对于两个通勤$ \ mathbb {r} $ - 动作，来自单个共同可测量的量度提供$ \ mathbb {r}^2 $ - 在概率空间上。证明的关键要素来自最近关于多线性奇异积分的工作。更具体地说，从对三角形希尔伯特变换的曲面模型的研究。
We prove a.e. convergence of continuous-time quadratic averages with respect to two commuting $\mathbb{R}$-actions, coming from a single jointly measurable measure-preserving $\mathbb{R}^2$-action on a probability space. The key ingredient of the proof comes from recent work on multilinear singular integrals; more specifically, from the study of a curved model for the triangular Hilbert transform.
