论文标题
关于超音
On superorthogonality
论文作者
论文摘要
在此调查中，我们探讨了序列$ f_1，f_2，f_3，\ ldots $中的超声函数如何导致相关的正方形功能导致直接或匡威不平等。我们区分了三种主要的超声类似物类型，我们证明了这在谐波分析和数字理论的各种环境中出现。这种观点提供了中心结果的简洁证明，并统一了主题，包括Khintchine的不平等，WALSH-PALEY系列，离散操作员，解耦，解耦，计算二聚体方程系统的解决方案，痕量函数的多相关以及Burgess绑定的短字符总和。
In this survey, we explore how superorthogonality amongst functions in a sequence $f_1,f_2,f_3,\ldots$ results in direct or converse inequalities for an associated square function. We distinguish between three main types of superorthogonality, which we demonstrate arise in a wide array of settings in harmonic analysis and number theory. This perspective gives clean proofs of central results, and unifies topics including Khintchine's inequality, Walsh-Paley series, discrete operators, decoupling, counting solutions to systems of Diophantine equations, multicorrelation of trace functions, and the Burgess bound for short character sums.
