Junyong Zhang

activity

20152025

most citedSobolev spaces adapted to the Schrödinger operator with inverse-square potential

12 citations · 28 across the 8 of their papers we have counts for

collaborators

9 papers

math.AP2025

Bochner-Riesz means on a conical singular manifold

Qiuye Jia, Junyong Zhang, Jiqiang Zheng

We prove a sharp $L^{p}$ -boundedness criterion for Bochner-Riesz multipliers on flat cones $X = (0, \infty) \times S_{σ}^{1}$ . The operator $S_{λ}^{δ} (Δ_{X})$ is bounded on $L^{p} (X)$ fo…

math.AP2025

Negative Order Bochner-Riesz Operators for the Critical Magnetic Schrödinger Operator in $R^{2}$

Huanqing Guo, Junyong Zhang, Jiqiang Zheng

This paper studies the sharp $L^{p}$ - $L^{q}$ boundedness of the Bochner-Riesz operator $S_{λ}^{δ} (L_{A})$ associated with a scaling-critical magnetic Schrödinger operato…

math.AP2025

$L^{p}$ -estimates for the 2D wave equation in the scaling-critical magnetic field

Jialu Wang, Fang Zhang, Junyong Zhang +1

In this paper, we study the $L^{p}$ -estimates for the solution to the $2 D$ -wave equation with a scaling-critical magnetic potential. Inspired by the work of \cite{FZZ}, we…

math.AP2024

Intertwining operators beyond the Stark Effect

Luca Fanelli, Xiaoyan Su, Ying Wang +2

The main mathematical manifestation of the Stark effect in quantum mechanics is the shift and the formation of clusters of eigenvalues when a spherical Hamiltonian is perturbed by…

math.AP2024

Pointwise dispersive estimates for Schrodinger and wave equations in a conical singular space

Qiuye Jia, Junyong Zhang

We study the pointwise decay estimates for the Schrödinger and wave equations on a product cone $(X, g)$ , where the metric $g = d r^{2} + r^{2} h$ and $X = C (Y) = (0, \infty) \times Y$ is a produc…

math.AP2024

Bochner-Riesz means for critical magnetic Schrödinger operators in $R^{2}$

Changxing Miao, Lixin Yan, Junyong Zhang

We study $L^{p}$ -boundedness of the Bochner-Riesz means for critical magnetic Schrödinger operators $\LL_{\A}$ in $R^{2}$ , which involve the {physical} Aharonov-Bohm potentia…

math.AP2017★ 7 cited

Global-in-time Strichartz estimates and cubic Schrödinger equation in a conical singular space

Junyong Zhang, Jiqiang Zheng

In this paper, we study Strichartz estimates for the Schrödinger equation on a metric cone $X$ , where $X = C (Y) = (0, \infty)_{r} \times Y$ and the cross section $Y$ is a $(n - 1)$ -dimension…

math.AP2015★ 9 cited

The energy-critical NLS with inverse-square potential

R. Killip, C. Miao, M. Visan +2

We consider the defocusing energy-critical nonlinear Schrödinger equation with inverse-square potential $i u_{t} = - Δ u + a ∣ x ∣^{- 2} u + ∣ u ∣^{4} u$ in three space dimensions. We prove globa…

math.AP2015★ 12 cited

Sobolev spaces adapted to the Schrödinger operator with inverse-square potential

R. Killip, C. Miao, M. Visan +2

We study the $L^{p}$ -theory for the Schrödinger operator $L_{a}$ with inverse-square potential $a ∣ x ∣^{- 2}$ . Our main result describes when $L^{p}$ -based Sobolev spaces defined i…

Bochner-Riesz means on a conical singular manifold

Negative Order Bochner-Riesz Operators for the Critical Magnetic Schrödinger Operator in R2

Lp-estimates for the 2D wave equation in the scaling-critical magnetic field

Intertwining operators beyond the Stark Effect

Pointwise dispersive estimates for Schrodinger and wave equations in a conical singular space

Bochner-Riesz means for critical magnetic Schrödinger operators in R2

Global-in-time Strichartz estimates and cubic Schrödinger equation in a conical singular space

The energy-critical NLS with inverse-square potential

Sobolev spaces adapted to the Schrödinger operator with inverse-square potential

Negative Order Bochner-Riesz Operators for the Critical Magnetic Schrödinger Operator in $R^{2}$

$L^{p}$ -estimates for the 2D wave equation in the scaling-critical magnetic field

Bochner-Riesz means for critical magnetic Schrödinger operators in $R^{2}$