On a conjecture of E.M. Stein on the Hilbert transform on vector fields
著者
書誌事項
On a conjecture of E.M. Stein on the Hilbert transform on vector fields
（Memoirs of the American Mathematical Society, no. 965）
American Mathematical Society, c2010
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注記
"Volume 205, number 965 (fourth of 5 numbers)."
Includes bibliographical references (p. 71-72)
内容説明・目次
内容説明
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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