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Publications (18)

math.FA2022

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

Shyam Swarup Mondal, Manli Song

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

math.FA2015

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.FA2024

Orthonormal Strichartz inequalities and their applications on abstract measure spaces

Guoxia Feng, Shyam Swarup Mondal, Manli Song +1

The main objective of this paper is to extend certain fundamental inequalities from a single function to a family of orthonormal systems. In the first part of the paper, we conside…

math.AP2024

Decay estimates and Strichartz inequalities for a class of dispersive equations on H-type groups

Manli Song, Jinggang Tan

Let $L$ be the sub-Laplacian on H-type groups and $I ¨ : R^{+} \to R$ be a smooth function. The primary objective of the paper is to study the decay estimat…

math.AP2025

Strichartz estimates for higher order SchrÃ¶dinger equations with Partial regular initial data

Vishvesh Kumar, Shyam Swarup Mondal, Iswarya Sitiraju +1

In this paper, we establish refined Strichartz estimates for higher-order SchrÃ¶dinger equations with initial data exhibiting partial regularity. By partial regularity, we mean tha…

math.FA2025

Orthonormal Strichartz estimates for Dunkl-SchrÃ¶dinger equation of initial data with Sobolev regularity

Guoxia Feng, Shyam Swarup Mondal, Manli Song +1

Let $I^_{I^} º$ be the Dunkl-Laplacian on $R^{n}$ . The main aim of this paper is to investigate the orthonormal Strichartz estimates for the SchrÃ¶dinger equation with initial d…

math.FA2014

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.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.FA2025

Local Dispersive and Strichartz estimates for the SchrÃ¶dinger equation associated to the Ornstein-Uhlenbeck operator

Aparajita Dasgupta, Uttam Kumar Dolai, Cheng Luo +1

In this paper we study the linear and nonlinear SchrÃ¶dinger equations associated with the Ornstein-Uhlenbeck (OU) operator endowed with the Gaussian measure. While classical Stric…

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 $(X, d, I^¼)$ is a metric space endowed with a non-negative Borel measure $I^¼$ satisfying the doubling condition and the additional condition that $I^¼ (B (x, r)) ≳ r^{n}$ …

math.AP2025

Strichartz estimates involving orthonormal systems at the critical summability exponent

Guoxia Feng, Manli Song, Huoxiong Wu

The primary objective of this paper is to investigate the orthonormal Strichartz estimates at the critical summability exponent for the SchrÃ¶dinger operator $e^{i t I^}$ with initia…

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_Î¼=\overset{d}{\underset{i=1}{\sum}}\partial_{x_i}^2+\left(\ov…

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 SchrÃ¶dinger propagator $e^{- i t L_{I^} \pm}$ for the Laguerre op…

math.FA2024

Decay estimates for a class of Dunkl wave equations

Cheng Luo, Shyam Swarup Mondal, Manli Song

Let $I^_{I^} º$ be the Dunkl Laplacian on $R^{n}$ and $I ¨ : R^{+} \to R$ is a smooth function. The aim of this manuscript is twofold. First, we study the decay es…

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 $e^{i t I^^{I^} \pm}$ , $0 < I^\pm < 1$ . Combing the dispersive estima…

math.AP2017

Strichartz inequalities for the SchrÃ¶dinger 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 SchrÃ¶dinger equation related to the full Laplacian on H-type groups. This exte…

math.AP2026

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

Jiabin Qian, Manli Song

Let $L_{a} = - I^_{x} - I^_{y} + \frac{a}{2} ∣ x ∣^{- 2}$ with $a > 0$ denote the SchrÃ¶dinger operator on $L^{2} (R_{x}^{2} \times R_{y}^{n})$ , which involves a singular partial inve…

math.AP2026

Dispersive decay for the mass-critical SchÃ¶dinger 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 SchrÃ¶dinger equation in spatial dimensions $d \geq 3$ . Our argument re…

Publications (18)

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

The restriction theorem for the Grushin operators

Orthonormal Strichartz inequalities and their applications on abstract measure spaces

Decay estimates and Strichartz inequalities for a class of dispersive equations on H-type groups

Strichartz estimates for higher order SchrÃ¶dinger equations with Partial regular initial data

Orthonormal Strichartz estimates for Dunkl-SchrÃ¶dinger equation of initial data with Sobolev regularity

A functional calculus and restriction theorem on H-type groups

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

Local Dispersive and Strichartz estimates for the SchrÃ¶dinger equation associated to the Ornstein-Uhlenbeck operator

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

Strichartz estimates involving orthonormal systems at the critical summability exponent

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

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

Decay estimates for a class of Dunkl wave equations

Decay estimates for fractional wave equations on H-type groups

Strichartz inequalities for the SchrÃ¶dinger equation with the full Laplacian on H-type groups

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

Dispersive decay for the mass-critical SchÃ¶dinger equation when d≥3

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

Dispersive decay for the mass-critical SchÃ¶dinger equation when $d \geq 3$