Hilbert transforms along variable planar curves: Lipschitz regularity
Abstract
In this paper, for $1<p<\infty$, we obtain the $L^p$boundedness of the Hilbert transform $H^{\gamma}$ along a variable plane curve $(t,u(x_1, x_2)\gamma(t))$, where $u$ is a Lipschitz function with small Lipschitz norm, and $\gamma$ is a general curve satisfying some suitable smoothness and curvature conditions.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 arXiv:
 arXiv:2104.12058
 Bibcode:
 2021arXiv210412058L
 Keywords:

 Mathematics  Classical Analysis and ODEs