Home » On a Conjecture of E.M. Stein on the Hilbert Transform on Vector Fields by Michael Lacey
On a Conjecture of E.M. Stein on the Hilbert Transform on Vector Fields Michael Lacey

On a Conjecture of E.M. Stein on the Hilbert Transform on Vector Fields

Michael Lacey

Published September 21st 2010
ISBN : 9780821845400
Paperback
72 pages
Enter the sum

 About the Book 

Let $v$ be a smooth vector field on the plane, that is a map from the plane to the unit circle. The authors study sufficient conditions for the boundedness of the Hilbert transform $/textrm{H}_{v, /epsilon }f(x): = /text{p.v.}/int_{-/epsilon}MoreLet $v$ be a smooth vector field on the plane, that is a map from the plane to the unit circle. The authors study sufficient conditions for the boundedness of the Hilbert transform $/textrm{H}_{v, /epsilon }f(x): = /text{p.v.}/int_{-/epsilon} DEGREES{/epsilon} f(x-yv(x))/-/frac{dy}y$ where $/epsilon$ is a suitably chosen parameter, determined by the smoothness properties of the vector field. Table of Contents: Overview of principal results- Besicovitch set and Carlesons theorem- The Lipschitz Kakeya maximal function- The $L DEGREES2$ estimate- Almost orthogonality between annuli.