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math.CA2003
Maximal Theorems for the Directional Hilbert Transform on the Plane
Michael T Lacey, Xiaochun Li
For a Schwartz function on the plane and a non-zero $v\in\ZR^2$ define the Hilbert transform of in the direction to be $$ H_vf(x)=\text{p.v.}\int_\ZR f(x-vy) \frac{dy}y…
math.CA2003
On the Hilbert Transform and $C^{1+\ze}$ Families of Lines
Michael T Lacey, Xiaochun Li
this paper has been withdrawn. A crucial estimate on a Lipschitz variant of the Kakeya maximal function has an incomplete proof.