Hilbert transform along measurable vector fields constant on Lipschitz curves: 𝐿^{𝑝} boundedness

Guo, Shaoming

doi:10.1090/tran/6750

Hilbert transform along measurable vector fields constant on Lipschitz curves: $L^p$ boundedness
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Trans. Amer. Math. Soc. 369 (2017), 2493-2519 Request permission

Abstract:

We prove the $L^p$ ($p>3/2$) boundedness of the directional Hilbert transform in the plane relative to measurable vector fields which are constant on suitable Lipschitz curves.

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