论文标题
步骤2的离散nilpotent组中的多项式序列
Polynomial sequences in discrete nilpotent groups of step 2
论文作者
论文摘要
我们讨论了我们在步骤2的Nilpotent组中沿多项式序列的平均值进行讨论的一些工作。我们的主要结果包括相关最大函数和奇异积分算子的界限，几乎到处都是沿多种序列的Ergodic平均值的点融合定理，以及多项式战争理论。 我们的证明基于分析工具，例如nilpotent Weyl不平等，以及旨在替换傅立叶变换工具的复杂几乎正交性参数，这些工具在非交通性的nilpotent设置中不可用。特别是，我们介绍了我们所谓的“ nilpotent Circle方法”，该方法使我们能够将古典圆方法的某些想法调整为nilpotent群体的设置。
We discuss some of our work on averages along polynomial sequences in nilpotent groups of step 2. Our main results include boundedness of associated maximal functions and singular integrals operators, an almost everywhere pointwise convergence theorem for ergodic averages along polynomial sequences, and a nilpotent Waring theorem. Our proofs are based on analytical tools, such as a nilpotent Weyl inequality, and on complex almost-orthogonality arguments that are designed to replace Fourier transform tools, which are not available in the non-commutative nilpotent setting. In particular, we present what we call a "nilpotent circle method" that allows us to adapt some of the ideas of the classical circle method to the setting of nilpotent groups.
