Hilbert transform along a C1+e vector field

Xiaochun Li

Let v be a vector field from R2 to the unit circle S1. We study the operator
Hvf(x) = p.v.

f(x-tv(x))  dt

We prove that if the vector field v has 1+e derivatives, then Hv extends to a bounded map from L2 onto itself.

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On 18 Feb 2004, 19:48.