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arXiv · 1605.08509

Restriction Theorem for Oscillatory Integral Operator with Certain Polynomial Phase

Shaozhen Xu·Dunyan Yan
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Abstract

We consider the following oscillatory integral operator \begin{equation}\label{opera-defi-1} T_{\alpha,m}f(x)=\int_{\mathbb R^n}e^{i(x_1^{\alpha_1} y_1^m+\cdots+x_n^{\alpha_n} y_n^m)}f(y)dy, \end{equation} where the function $f$ is a Schwartz function. In this paper, the restriction theorem on $\mathbb{S}^{n-1}$ for this operator is obtained. Moreover, we obtain a necessary condition which ensures the restriction theorem hold.

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Shaozhen Xu, Dunyan Yan. 2016-05-27. Restriction Theorem for Oscillatory Integral Operator with Certain Polynomial Phase. https://doi.org/10.1007/s11464-017-0637-0

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