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Mathematics (1)

k-plane transform

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Bilinear identities involving the k-plane transform and Fourier extension operators
Part of
- Partial differential equations
- Harmonic analysis in several variables
David Beltran, Luis Vega
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 6 / December 2020

Published online by Cambridge University Press:

27 January 2020, pp. 3349-3377

Print publication:

December 2020
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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.