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Item Details
| Title:
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ON A CONJECTURE OF E. M. STEIN ON THE HILBERT TRANSFORM ON VECTOR FIELDS
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| By: |
Michael Lacey (Editor), Xiaochun Li (Editor) |
| Format: |
Paperback |
| List price:
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£67.50 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821845403 |
| ISBN 13: |
9780821845400 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 May, 2010 |
| Edition: |
New ed. |
| Series: |
Memoirs of the American Mathematical Society v. 205, No. 965 |
| Pages: |
72 |
| Description: |
Studies 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. |
| 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 $\textrm{H}_{v, \epsilon }f(x) := \text{p.v.}\int_{-\epsilon}^{\epsilon} f(x-yv(x))\;\frac{dy}y$ 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) |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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