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 PDF

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

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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