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arXiv · 2308.05631

Some new decay estimates for $(2+1)$-dimensional degenerate oscillatory integral operators

Yuxin Tan·Shaozhen Xu
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Abstract

In this paper, we consider the $(2+1)-$dimensional oscillatory integral operators with cubic homogeneous polynomial phases, which are degenerate in the sense of \cite{Tan06}. We improve the previously known $L^2\to L^2$ decay rate to $3/8$ and also establish a sharp $L^2\to L^6$ decay estimate based on fractional integration method.

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Yuxin Tan, Shaozhen Xu. 2023-08-10. Some new decay estimates for $(2+1)$-dimensional degenerate oscillatory integral operators. https://arxiv.org/abs/2308.05631

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