Colloquium
4:00 p.m., Thursday
(February 26th)
Math Bldg. Room 229
Xiaochun Li
University of California, Los Angeles
Hilbert transform along a C^{1+\epsilon} vector field
Let v be a vector field from {\mathbb{R}}^2 to the unit circle
{\mathbb{S}}^1. We study the operator
H_vf(x)=p.v.\int_{1}^1 f(xtv(x)) \frac{dt}{t} .
We prove that if the vector field v has 1+\epsilon derivatives,
then H_v extends to a bounded map from L^2 onto itself.
Refreshments will be served at 3:45 p.m. in the Faculty
Lounge, Math Annex (Room 1115).
