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

Published online by Cambridge University Press:  27 January 2020

David Beltran
Affiliation:
Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI53706, USA ([email protected])
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 ([email protected], [email protected])

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.

Type
Research Article
Copyright
Copyright © 2020 The Royal Society of Edinburgh

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