Pointwise convergence of certain continuous-time double ergodic averages
Pointwise convergence of certain continuous-time double ergodic averages
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DOI：
10.1017/etds.2021.45
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发表时间：
2020-11
影响因子：
0.9
通讯作者：
M. Christ;Polona Durcik;Vjekoslav Kovač;J. Roos
中科院分区：
文献类型：
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作者：
M. Christ;Polona Durcik;Vjekoslav Kovač;J. Roos
摘要我们证明了连续时间二次平均值关于两个交换$\mathbb {R}$ -作用的几乎处处收敛性，这两个交换$\mathbb {R}^2 $ -作用来自于概率空间上的一个联合可测的保测度$\mathbb {R}^2 $ -作用.证明的关键成分来自最近的工作多线性奇异积分，更具体地说，从三角希尔伯特变换的弯曲模型的研究。
Abstract We prove almost everywhere 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.