
eBook ISBN: | 978-1-4704-0579-3 |
Product Code: | MEMO/205/965.E |
List Price: | $68.00 |
MAA Member Price: | $61.20 |
AMS Member Price: | $40.80 |

eBook ISBN: | 978-1-4704-0579-3 |
Product Code: | MEMO/205/965.E |
List Price: | $68.00 |
MAA Member Price: | $61.20 |
AMS Member Price: | $40.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 205; 2010; 72 ppMSC: Primary 42
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 \[\mathrm{H}_{v, \epsilon }f(x) := \text{p.v.}\int_{-\epsilon}^{\epsilon} f(x-yv(x))\;\frac{dy}y\] where \(\epsilon\) is a suitably chosen parameter, determined by the smoothness properties of the vector field.
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Table of Contents
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Chapters
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Preface
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1. Overview of principal results
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2. Besicovitch set and Carleson’s Theorem
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3. The Lipschitz Kakeya maximal function
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4. The $ L^2$ estimate
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5. Almost orthogonality between annuli
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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 \[\mathrm{H}_{v, \epsilon }f(x) := \text{p.v.}\int_{-\epsilon}^{\epsilon} f(x-yv(x))\;\frac{dy}y\] where \(\epsilon\) is a suitably chosen parameter, determined by the smoothness properties of the vector field.
-
Chapters
-
Preface
-
1. Overview of principal results
-
2. Besicovitch set and Carleson’s Theorem
-
3. The Lipschitz Kakeya maximal function
-
4. The $ L^2$ estimate
-
5. Almost orthogonality between annuli