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Endpoint Mapping Properties of Wave Operators for Schrödinger Operators in Dimensions
Han Cheng, Changxing Miao, Xiaohua Yao
We study endpoint mapping properties of low-energy wave operators for Schrödinger operators on , . In dimension four, we prove that a zero-energy reson…
The Szemerédi-Trotter Estimate in Finite Field with its Applications
Changxing Miao, Rui Xie
We prove a sharp Szemerédi-Trotter estimate \[\mathcal{I}(A,\mathcal{L})\lesssim \frac{|A||\mathcal{L}|}{p}+|A|^{2/3}|\mathcal{L}|^{2/3}+|A|+|\mathcal{L}|\] for prime finite field…
Endpoint Mapping Properties of Wave Operators for Two-Dimensional Schrödinger Operators
Han Cheng, Changxing Miao, Xiaohua Yao
We establish sharp endpoint mapping properties for the wave operators of two-dimensional Schrödinger operators with real-valued decaying potentials . Toge…
A multidimensional Szemerédi theorem in integers
Jingwei Guo, Changxing Miao, Guoqing Zhan
For any integer , let be a strictly increasing -tuple of positive integers. We show that any subset of density at least $(\log…