On a conjecture of E.M. Stein on the Hilbert transform on vector fields /
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| Author / Creator: | Lacey, Michael T. (Michael Thoreau) |
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| Imprint: | Providence, R.I. : American Mathematical Society, 2010. |
| Description: | viii, 72 p. : ill. ; 26 cm. |
| Language: | English |
| Series: | Memoirs of the American Mathematical Society, 0065-9266 ; no. 965 Memoirs of the American Mathematical Society ; no. 965. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7998151 |
| Summary: | 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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| Item Description: | "Volume 205, number 965 (fourth of 5 numbers)." |
| Physical Description: | viii, 72 p. : ill. ; 26 cm. |
| Bibliography: | Includes bibliographical references (p. 71-72). |
| ISBN: | 9780821845400 0821845403 |
| ISSN: | 0065-9266 ; |
