A note on the cone restriction conjecture

Miao, Changxing; Zhang, Junyong; Zheng, Jiqiang

doi:10.1090/S0002-9939-2011-11076-1

A note on the cone restriction conjecture
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by Changxing Miao, Junyong Zhang and Jiqiang Zheng

Proc. Amer. Math. Soc. 140 (2012), 2091-2102

DOI: https://doi.org/10.1090/S0002-9939-2011-11076-1

Published electronically: October 20, 2011

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Abstract:

This paper is devoted to the study of the restriction problem in harmonic analysis. Based on the spherical harmonics expansion and analyzing the asymptotic behavior of the Bessel function, we show that a modified linear adjoint restriction estimate holds for all Schwartz functions compactly supported on the cone, which generalizes Shao’s result.

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