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Bilinear identities involving the k-plane transform and Fourier extension operators
Published online by Cambridge University Press: 27 January 2020
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.
MSC classification
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- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 6 , December 2020 , pp. 3349 - 3377
- Copyright
- Copyright © 2020 The Royal Society of Edinburgh
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