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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Uniform estimates for the local restriction of the Fourier transform to curves


Authors: Spyridon Dendrinos and Detlef Müller
Journal: Trans. Amer. Math. Soc. 365 (2013), 3477-3492
MSC (2010): Primary 42B10
Published electronically: December 17, 2012
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Abstract: We prove sharp estimates, with respect to the affine arclength measure, for the restriction of the Fourier transform to a class of curves in $ \mathbb{R}^d$ that includes curves of finite type. This measure possesses certain invariance and mitigation properties which are important in establishing uniform results.


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Additional Information

Spyridon Dendrinos
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), 40014 Jyväskylä, Finland
Address at time of publication: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68 (Gustaf Hällströmin katu 2b), 00014 Helsinki, Finland
Email: spyridon.dendrinos@jyu.fi, spyridon.dendrinos@helsinki.fi

Detlef Müller
Affiliation: Mathematisches Seminar, C. A.-Universität Kiel, Ludewig-Meyn-Strasse 4, 24098 Kiel, Germany
Email: mueller@math.uni-kiel.de

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05769-2
PII: S 0002-9947(2012)05769-2
Received by editor(s): June 15, 2011
Published electronically: December 17, 2012
Additional Notes: This research was partly carried out during a visit of the first author to the University of Kiel, funded by the Deutscher Akademischer Austausch Dienst (DAAD)
Article copyright: © Copyright 2012 American Mathematical Society