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An affine-invariant inequality for rational functions and applications in harmonic analysis

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  12 August 2010

Spyridon Dendrinos ,
Magali Folch-Gabayet  and
James Wright
Spyridon Dendrinos
Affiliation:
Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW, UK ([email protected])
Magali Folch-Gabayet
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Area de la Investigación Científica, Circuito Exterior, Ciudad Universitaria, DF 04510, Mexico ([email protected])
James Wright
Affiliation:
Maxwell Institute for Mathematical Sciences, The University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Edinburgh EH9 3JZ, UK ([email protected])
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Abstract

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We extend an affine-invariant inequality for vector polynomials established by Dendrinos and Wright to general rational functions. As a consequence we obtain sharp universal estimates for various problems in Euclidean harmonic analysis defined with respect to the so-called affine arc-length measure.

Keywords

affine-invariant inequalityrational functionsFourier restriction

MSC classification

Secondary: 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 3 , October 2010 , pp. 639 - 655
Copyright
Copyright © Edinburgh Mathematical Society 2010

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