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On a Conjecture of E. M. Stein on the Hilbert Transform on Vector Fields
 
Michael Lacey Georgia Institute of Technology, Atlanta, GA
Xiaochun Li University of Illinois, Urbana, Urbana, IL
On a Conjecture of E. M. Stein on the Hilbert Transform on Vector Fields
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
On a Conjecture of E. M. Stein on the Hilbert Transform on Vector Fields
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On a Conjecture of E. M. Stein on the Hilbert Transform on Vector Fields
Michael Lacey Georgia Institute of Technology, Atlanta, GA
Xiaochun Li University of Illinois, Urbana, Urbana, IL
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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2052010; 72 pp
    MSC: 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.

  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
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Volume: 2052010; 72 pp
MSC: 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.

  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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