ENGLISH

On a conjecture of E.M.Stein on the Hilbert transform on vector fields

By Xiaochun Li , Michael Lacey

Book information

Publisher
Amer Mathematical Society
Year
2010
ISBN
0821845403, 978-0-8218-4540-0
Language
english
Format
PDF
Filesize
671 kB (686888 bytes)
Series
Memoirs of the American Mathematical Society 0965
Pages
87\87
Library
kolxoz
Time added
2015-12-12 14:00:00

Description

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 $\textrm{H}_{v, \epsilon }f(x) := \text{p.v.}\int_{-\epsilon}^{\epsilon} f(x-yv(x))\;\frac{dy}y$ 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 Carleson's theorem; The Lipschitz Kakeya maximal function; The $L^2$ estimate; Almost orthogonality between annuli. (MEMO/205/965)

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