Remarks on a nonlocal transport

Dong Li; Jose Rodrigo

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arXiv · 2002.11305

Remarks on a nonlocal transport

Dong Li·Jose Rodrigo

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Abstract

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.

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Dong Li, Jose Rodrigo. 2020-02-26. Remarks on a nonlocal transport. https://arxiv.org/abs/2002.11305

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