Norm variation of ergodic averages with respect to two commuting transformations
Norm variation of ergodic averages with respect to two commuting transformations
复制标题
关于两个通勤变换的遍历平均值的范数变化
DOI：
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发表时间：
2016
影响因子：
0.9
通讯作者：
C. Thiele
中科院分区：
文献类型：
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作者：
Polona Durcik;Vjekoslav Kovač;Kristina Ana Škreb;C. Thiele
我们研究了关于两种一般交换变换的双遍历平均，并建立了它们在范数上收敛的一个清晰的定量结果。我们利用最近发展的具有一定纠缠结构的边界多重线性奇异积分的方法，通过实调和分析来解决这个问题。我们证明的副产品是一个二维双线性平方函数的界与所谓的三角希尔伯特变换有关。
We study double ergodic averages with respect to two general commuting transformations and establish a sharp quantitative result on their convergence in the norm. We approach the problem via real harmonic analysis, using recently developed methods for bounding multilinear singular integrals with certain entangled structure. A byproduct of our proof is a bound for a two-dimensional bilinear square function related to the so-called triangular Hilbert transform.