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Hilbert transforms along variable planar curves: Lipschitz regularity (2104.12058v1)

Published 25 Apr 2021 in math.CA

Abstract: In this paper, for $1<p<\infty$, we obtain the $Lp$-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.

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