调和分析中的离散类似物：多参数拉东平均值
Discrete analogues in harmonic analysis: Multi-parameter Radon averages
AI总结：
研究多参数离散拉东平均算子的极大值和振荡不等式，通过开发多参数圆法的稳健变体给出定量估计，解决了遍历理论中的多参数贝洛 - 弗斯滕伯格问题。
AI中文摘要：
本文研究多参数离散拉东平均算子的极大值和振荡不等式。我们在调和分析离散类似物框架内开发了多参数圆法的稳健变体。这给出了这些平均值及其基础傅里叶乘子的定量估计，揭示了有趣的主弧刚性现象。结果，我们肯定地完全解决了遍历理论中的多参数贝洛 - 弗斯滕伯格问题。
英文摘要：
In this paper we study maximal and oscillation inequalities for multi-parameter discrete Radon averaging operators. We develop a robust variant of the multi-parameter circle method within the framework of Discrete Analogues in Harmonic Analysis. In particular, this gives quantitative estimates for these averages and their underlying Fourier multipliers which reveals an interesting major-arcs rigidity phenomenon. As a consequence, we completely resolve in the affirmative the multi-parameter Bellow--Furstenberg problem in pointwise ergodic theory.
