eBook ISBN:  9781470405793 
Product Code:  MEMO/205/965.E 
List Price:  $68.00 
MAA Member Price:  $61.20 
AMS Member Price:  $40.80 
eBook ISBN:  9781470405793 
Product Code:  MEMO/205/965.E 
List Price:  $68.00 
MAA Member Price:  $61.20 
AMS Member Price:  $40.80 

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 \[\mathrm{H}_{v, \epsilon }f(x) := \text{p.v.}\int_{\epsilon}^{\epsilon} f(xyv(x))\;\frac{dy}y\] where \(\epsilon\) is a suitably chosen parameter, determined by the smoothness properties of the vector field.

Table of Contents

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


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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 \[\mathrm{H}_{v, \epsilon }f(x) := \text{p.v.}\int_{\epsilon}^{\epsilon} f(xyv(x))\;\frac{dy}y\] 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