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A NOTE ON LOCALISED WEIGHTED INEQUALITIES FOR THE EXTENSION OPERATOR

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  01 June 2008

J. A. BARCELÓ ,
J. M. BENNETT  and
A. CARBERY
J. A. BARCELÓ
Affiliation:
ETSI de Caminos, Universidad Politécnica de Madrid, 28040, Madrid, Spain (email: [email protected])
J. M. BENNETT*
Affiliation:
School of Mathematics, The Watson Building, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK (email: [email protected])
A. CARBERY
Affiliation:
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, JCMB, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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We prove optimal radially weighted L2-norm inequalities for the Fourier extension operator associated to the unit sphere in ℝn. Such inequalities valid at all scales are well understood. The purpose of this short paper is to establish certain more delicate single-scale versions of these.

Keywords

Fourier extension operatorsweighted inequalities

MSC classification

Secondary: 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 3 , June 2008 , pp. 289 - 299
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

All authors were supported by the EC project ‘HARP’. The first was also supported by Spanish Grant BFM02206, the second by EPSRC Postdoctoral Fellowship GR/S27009/02 and the third by a Leverhulme Study Abroad Fellowship and EC project ‘Pythagoras’.

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