发表机构
University of Science and Technology of China; University of Illinois at Urbana-Champaign（中国科学技术大学; 伊利诺伊大学厄巴纳-香槟分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过建立多线性仿积的一致估计并应用索伯列夫平滑不等式，证明了沿矩曲线的多线性希尔伯特变换及其极大函数的有界性。
AI 中文摘要
我们通过建立平移和非平移多线性仿积的一致估计，并应用索伯列夫平滑不等式，证明了沿矩曲线的多线性希尔伯特变换的有界性。作为我们方法的副产品，我们获得了沿矩曲线的多线性极大函数的相同界。
英文摘要
We prove the boundedness of multilinear Hilbert transforms along moment curves by establishing uniform estimates for both translated and untranslated multilinear paraproducts and by applying a Sobolev smoothing inequality. As a byproduct of our method, we obtain the same bounds for multilinear maximal functions along moment curves.
CommentsThe lower bound 1/3 for r in the first version is corrected to 1/2 due to counterexamples, which are provided. A uniform estimate for the corresponding multilinear Hilbert transform is added. Some typos are corrected, and more details are added to the proofs of several lemmas
