Xiangrong Zhu

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math.CA2024

Endpoint regularity of general Fourier integral operators

Xiangrong Zhu, Wenjuan Li

Let $n \geq 1, 0 < ρ < 1, max {ρ, 1 - ρ} \leq δ \leq 1$ and $m_{1} = ρ - n + (n - 1) min {\frac{1}{2}, ρ} + \frac{1 - δ}{2} .$ If the amplitude $a$ belongs to the Hörmander class $S_{ρ, δ}^{m_{1}}$ and $ϕ\in…

math.CA2023

$L^{p}$ boundedness of pseudo-differential operators with symbols in $S_{ρ, 1}^{n (ρ - 1) /2}$

Jingwei Guo, Xiangrong Zhu

For symbol $a \in S_{ρ, 1}^{n (ρ - 1) /2}$ the pseudo-differential operator $T_{a}$ may not be $L^{2}$ bounded. However, under some mild extra assumptions on $a$ , we show that $T_{a}$ is bound…

Endpoint regularity of general Fourier integral operators

Lp boundedness of pseudo-differential operators with symbols in Sρ,1n(ρ−1)/2​

$L^{p}$ boundedness of pseudo-differential operators with symbols in $S_{ρ, 1}^{n (ρ - 1) /2}$