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Bilinear identities involving the k-plane transform and Fourier extension operators

Part of: Partial differential equations Harmonic analysis in several variables

Published online by Cambridge University Press:  27 January 2020

David Beltran  and
Luis Vega
David Beltran
Affiliation:
Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI53706, USA (dbeltran@math.wisc.edu)
Luis Vega
Affiliation:
Departamento de Matematicas, Universidad del Pais Vasco/Euskal Herriko Unibertsitatea (UPV/EHU), Aptdo. 644, Bilbao48080, Spain Basque Center for Applied Mathematics (BCAM), Alameda de Mazarredo 14, Bilbao48009, Spain (lvega@bcamath.org, luis.vega@ehu.es)
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Abstract

We prove certain L2(ℝn) bilinear estimates for Fourier extension operators associated to spheres and hyperboloids under the action of the k-plane transform. As the estimates are L2-based, they follow from bilinear identities: in particular, these are the analogues of a known identity for paraboloids, and may be seen as higher-dimensional versions of the classical L2(ℝ2)-bilinear identity for Fourier extension operators associated to curves in ℝ2.

Keywords

k-plane transformFourier extension operatorsbilinear identities

MSC classification

Primary: 42B37: Harmonic analysis and PDE
Secondary: 35A23: Inequalities involving derivatives and differential and integral operators, inequalities for integrals
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 6 , December 2020 , pp. 3349 - 3377
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Copyright
Copyright © 2020 The Royal Society of Edinburgh

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