On a conjecture of E.M.Stein on the Hilbert transform on vector fields
Michael Lacey, Xiaochun Li
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)
Categorie:
Anno:
2010
Casa editrice:
Amer Mathematical Society
Lingua:
english
Pagine:
87
ISBN 10:
0821845403
ISBN 13:
9780821845400
Collana:
Memoirs of the American Mathematical Society 0965
File:
PDF, 671 KB
IPFS:
,
english, 2010
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