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Remarks on a nonlocal transport
Advances in Mathematics ( IF 1.7 ) Pub Date : 2020-11-01 , DOI: 10.1016/j.aim.2020.107345
Dong Li , Jose Rodrigo

We consider a one dimensional nonlocal transport equation and its natural multi-dimensional analogues. By using a new pointwise inequality for the Hilbert transform, we give a short proof of a nonlinear inequality first proved by C\'{o}rdoba, C\'{o}rdoba and Fontelos in 2005. We also prove several new weighted inequalities for the Hilbert transform and various nonlinear versions. Some of these results generalize to a related family of nonlocal models.

中文翻译:

关于非本地运输的备注

我们考虑一维非局部传输方程及其自然的多维类似物。通过对希尔伯特变换使用新的逐点不等式,我们给出了非线性不等式的简短证明,该非线性不等式最初由 C\'{o}rdoba, C\'{o}rdoba 和 Fontelos 在 2005 年证明。我们还证明了几个新的加权不等式用于希尔伯特变换和各种非线性版本。其中一些结果推广到相关的非局部模型系列。
更新日期:2020-11-01
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