On a Conjecture of E. M. Stein on the Hilbert Transform on Vector Fields (Memoirs of the American Mathematical Society)

Lacey, Michael; Li, Xiaochun

ISBN 10: 0821845403 / ISBN 13: 9780821845400

Published by Amer Mathematical Society, 2010

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Bibliographic Details

• Title: On a Conjecture of E. M. Stein on the Hilbert Transform on Vector Fields (Memoirs of the American Mathematical Society)
• Publisher: Amer Mathematical Society
• Publication Date: 2010
• Language: English
• ISBN 10: 0821845403
• ISBN 13: 9780821845400
• Binding: Soft cover
• Condition: As New

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Synopsis

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 $ extrm{H}_{v, psilon }f(x): = ext{p.v.}int_{- psilon} DEGREES{ psilon} f(x-yv(x)); rac{dy}y$ where $ psilon$ is a suitably chosen parameter, determined by the smoothness properties of the vector field. Table of Contents: Overview of principal results; Besicovitch set and Carleson's theorem; The Lipschitz Kakeya maximal function; The $L DEGREES2$ estimate; Almost orthogonality between annuli.