Manli Song

activity

20142026

most citedA functional calculus and restriction theorem on H-type groups

4 citations · 7 across the 10 of their papers we have counts for

collaborators

11 papers

math.AP2026

Decay estimates for a class of dispersive equations with partial inverse-square potentials

Jiabin Qian, Manli Song

Let $L_{a} = - Δ_{x} - Δ_{y} + \frac{a}{2} ∣ x ∣^{- 2}$ with $a > 0$ denote the Schrödinger operator on $L^{2} (R_{x}^{2} \times R_{y}^{n})$ , which involves a singular partial inverse…

math.AP2026

Dispersive decay for the mass-critical Schödinger equation when $d \geq 3$

Jiabin Qian, Manli Song

In this paper we establish the pointwise-in-time dispersive decay for solutions to the mass-critical nonlinear Schrödinger equation in spatial dimensions $d \geq 3$ . Our argument rel…

math.AP2023

Decay estimates for a class of semigroups related to self-adjoint operators on metric measure spaces

Guoxia Feng, Manli Song, Huoxiong Wu

Assume that $(X, d, μ)$ is a metric space endowed with a non-negative Borel measure $μ$ satisfying the doubling condition and the additional condition that $μ (B (x, r)) ≳ r^{n}$ for…

math.FA2022★ 1 cited

Orthonormal Strichartz inequalities for the $(k, a)$ -generalized Laguerre operator and Dunkl operator

Shyam Swarup Mondal, Manli Song

Let $Δ_{k, a}$ and $Δ_{k}$ be the $(k, a)$ -generalized Laguerre operator and the Dunkl Laplacian operator on $R^{n}$ , respectively. The aim of this article is twofold. First, w…

math.FA2022

Restriction theorems and Strichartz inequalities for the Laguerre operator involving orthonormal functions

Guoxia Feng, Manli Song

In this paper, we prove restriction theorems for the Fourier-Laguerre transform and establish Strichartz estimates for the Schrödinger propagator $e^{- i t L_{α}}$ for the Laguerre oper…

math.AP2022

Decay estimates for a class of wave equations on the Heisenberg group

Manli Song, Jiale Yang

In this paper, we study a class of dispersive wave equations on the Heisenberg group $H^{n}$ . Based on the group Fourier transform on $H^{n}$ , the properties of the Laguerre functions…

math.FA2016

Decay estimates for fractional wave equations on H-type groups

Manli Song

The aim of this paper is to establish the decay estimate for the fractional wave equation semigroup on H-type groups given by $e^{i t Δ^{α}}$ , $0 < α < 1$ . Combing the dispersive estimate…

math.AP2016

Weighted Caffarelli-Kohn-Nirenberg type inequalities related to Grushin type operators

Manli Song, Wenjuan Li

We consider the Grushin type operator on $R_{x}^{d} \times R_{y}^{k}$ with the form \begin{equation*} G_μ=\overset{d}{\underset{i=1}{\sum}}\partial_{x_i}^2+\left(\ove…

math.FA2014★ 4 cited

A functional calculus and restriction theorem on H-type groups

Heping Liu, Manli Song

Let $L$ be the sublaplacian and $T$ the partial Laplacian with respect to central variables on H-type groups. We investigate a class of invariant differential operators by the join…

math.FA2014★ 2 cited

The restriction theorem for the Grushin operators

Heping Liu, Manli Song

We study the Grushin operators acting on $R_{x}^{d_{1}} \times R_{t}^{d_{2}}$ and defined by the formula \begin{equation*} L=-\overset{d_1}{\underset{j=1}{\sum}}\partial_…

math.AP2014

Strichartz inequalities for the Schrödinger equation with the full Laplacian on H-type groups

Manli Song

In this paper, we prove the dispersive estimates and Strichartz inequalities for the solution of the Schrödinger equation related to the full Laplacian on H-type groups. This exten…

Decay estimates for a class of dispersive equations with partial inverse-square potentials

Dispersive decay for the mass-critical Schödinger equation when d≥3

Decay estimates for a class of semigroups related to self-adjoint operators on metric measure spaces

Orthonormal Strichartz inequalities for the (k,a)-generalized Laguerre operator and Dunkl operator

Restriction theorems and Strichartz inequalities for the Laguerre operator involving orthonormal functions

Decay estimates for a class of wave equations on the Heisenberg group

Decay estimates for fractional wave equations on H-type groups

Weighted Caffarelli-Kohn-Nirenberg type inequalities related to Grushin type operators

A functional calculus and restriction theorem on H-type groups

The restriction theorem for the Grushin operators

Strichartz inequalities for the Schrödinger equation with the full Laplacian on H-type groups

Dispersive decay for the mass-critical Schödinger equation when $d \geq 3$

Orthonormal Strichartz inequalities for the $(k, a)$ -generalized Laguerre operator and Dunkl operator