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A sharp decay estimate for degnerate oscillatory integral operators using broad-narrow method
Shaozhen Xu
We use broad-narrow method to estabish the sharp decay estimate for a class of degenerate oscillatory integral operators in dimensions. Especially, the model phase fu…
Damping estimates for oscillatory integral operators with real-analytic phases and its applications
Zuoshunhua Shi, Shaozhen Xu, Dunyan Yan
In this paper, we investigate sharp damping estimates for a class of one dimensional oscillatory integral operators with real-analytic phases. By establishing endpoint estimates fo…
The sharp decay of oscillatory integral operators with certain homogeneous polynomial phases in several variables
Shaozhen Xu, Dunyan Yan
We obtain the decay of oscillatory integral operators with certain homogeneous polynomial phase of degree in -dimensions. In this paper we require that $d>2n…
Restriction Theorem for Oscillatory Integral Operator with Certain Polynomial Phase
Shaozhen Xu, Dunyan Yan
We consider the following oscillatory integral operator \begin{equation}\label{opera-defi-1} T_{α,m}f(x)=\int_{\mathbb R^n}e^{i(x_1^{α_1} y_1^m+\cdots+x_n^{α_n} y_n^m)}f(y)dy, \end…