论文标题
关于非本地运输的评论
Remarks on a nonlocal transport
论文作者
论文摘要
我们考虑一个维度非局部传输方程及其自然的多维类似物。通过对希尔伯特转变使用新的不平等现象，我们简短地证明了Córdoba，Córdoba和Fontelos在2005年首先证明了非线性不平等。其中一些结果推广到相关的非本地模型家族。
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 Córdoba, Córdoba 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.
