论文标题
沿多项式生长的平滑函数中的尼尔曼群岛的侧面收敛
Pointwise convergence in nilmanifolds along smooth functions of polynomial growth
论文作者
论文摘要
我们研究了nilmanifold $ x $中$ b_1^{a_1（n）} $ b_1^{a_1（n）}的轨道的等分分布。我们表明，在某些假设上，这些函数的增长率$ a_1，...，a_k $，这些轨道均匀地分布在空间$ x $的某些子尼尔曼福尔德上。作为这些结果的应用，并结合了用于测量系统的HOST-KRA结构定理，以及对hardy场功能的Ergodic平均作者的一些最新的静态估计，我们推断出多个ergodic平均值的规范收敛结果。我们的方法主要取决于绿色tao在尼尔曼群岛的有限多项式轨道上的等分分配结果。
We study the equidistribution of orbits of the form $b_1^{a_1(n)}... b_k^{a_k(n)}Γ$ in a nilmanifold $X$, where the sequences $a_i(n)$ arise from smooth functions of polynomial growth belonging to a Hardy field. We show that under certain assumptions on the growth rates of the functions $a_1,...,a_k$, these orbits are uniformly distributed on some subnilmanifold of the space $X$. As an application of these results and in combination with the Host-Kra structure theorem for measure preserving systems, as well as some recent seminorm estimates of the author for ergodic averages concerning Hardy field functions, we deduce a norm convergence result for multiple ergodic averages. Our method mainly relies on an equidistribution result of Green-Tao on finite polynomial orbits of a nilmanifold.
