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(x-tv(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).