Shaozhen Xu

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20232026

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math.CA2026

Sharp decay estimates for $(2 + 1)$ -dimensional oscillatory integral operators via Newton height

Shaozhen Xu

We study $(2 + 1)$ -dimensional oscillatory integral operators of the form \[ T_λf(x,y)=\int_{\mathbb{R}}e^{iλP(x,y)t^k}ψ(x,y,t)f(t)dt,\qquad k\geq 1, \] where the phase $P$ is a real…

math.CA2025

An effective van der Corput-type method in higher dimensions

Shaozhen Xu

Using the birational map between a smooth toric variety (adapted to the phase function of the oscillatory integral) and $\mathbb{R}^n\textbackslash\{0\}$, we can effectively carry…

math.CA2024

Some sharp $L^{2} \to L^{p}$ decay estimates for $(2 + 1)$ -dimensional degenerate oscillatory integral operators

Shaozhen Xu

We investigate $(2 + 1) -$ dimensional oscillatory integral operators characterized by polynomial phase functions. By employing Stein's complex interpolation, we derive sharp $L^2\to L…

math.CA2023

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

Yuxin Tan, Shaozhen Xu

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 im…

Sharp decay estimates for (2+1)-dimensional oscillatory integral operators via Newton height

An effective van der Corput-type method in higher dimensions

Some sharp L2→Lp decay estimates for (2+1)-dimensional degenerate oscillatory integral operators

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

Sharp decay estimates for $(2 + 1)$ -dimensional oscillatory integral operators via Newton height

Some sharp $L^{2} \to L^{p}$ decay estimates for $(2 + 1)$ -dimensional degenerate oscillatory integral operators

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