Hilbert transform along a C^{1+e} vector field
Xiaochun Li
Let v be a vector field from R^{2} to the unit circle
S^{1}.
We study the operator
H_{v}f(x) = p.v. 
ó õ

1
1

f(xtv(x)) 
dt
t

. 

We prove that if the vector field v has 1+e derivatives,
then H_{v} extends to a bounded map from L^{2} onto itself.
File translated from
T_{E}X
by
T_{T}H,
version 3.06.
On 18 Feb 2004, 19:48.