Liang Song

activity

20112026

most citedBoundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity

15 citations · 32 across the 21 of their papers we have counts for

collaborators

22 papers

math.AP2026

Fefferman--Stein type inequalities via area and maximal functions for Schrödinger operators with applications

Ji Li, Wanjun Li, Liang Song +1

In this paper, we establish a Fefferman--Stein inequality in terms of area function and non-tangential maximal function associated with the Schrödinger operator $\mathcal{L} = -Δ+…

math.CA2023

The Garnett-Jones Theorem on BMO spaces associated with operators and applications

Peng Chen, Xuan Thinh Duong, Ji Li +2

Let $X$ be a metric space with doubling measure, and $L$ be a nonnegative self-adjoint operator on $L^{2} (X)$ whose heat kernel satisfies the Gaussian upper bound. Let $f$ be in the…

math.AP2022

Dirichlet problem for Schrödinger operators on Heisenberg groups

Ji Li, Qingze Lin, Liang Song

We investigate the Dirichlet problem associated to the Schrödinger operator $L = - Δ_{H^{n}} + V$ on Heisenberg group $H^{n}$ : \begin{align*} \begin{cases} \partia…

math.AP2022

Pointwise Decay of solutions to the energy critical nonlinear Schrödinger equations

Zihua Guo, Chunyan Huang, Liang Song

In this note, we prove pointwise decay in time of solutions to the 3D energy-critical nonlinear Schrödinger equations assuming data in $L^{1} \cap H^{3}$ . The main ingredients are the b…

math.CA2021

The CMO-Dirichlet problem for the Schrödinger equation in the upper half-space and characterizations of CMO

Liang Song, Liangchuan Wu

Let $L$ be a Schrödinger operator of the form $L = - Δ + V$ acting on $L^{2} (R^{n})$ where the nonnegative potential $V$ belongs to the reverse Hölder class ${RH…

math.CA2020★ 1 cited

$L^{p} (R^{2})$ -boundedness of Hilbert Transforms and Maximal Functions along Plane Curves with Two-variable Coefficients

Naijia Liu, Liang Song, Haixia Yu

In this paper, for general plane curves $γ$ satisfying some suitable smoothness and curvature conditions, we obtain the single annulus $L^{p} (R^{2})$ -boundedness of the Hilber…

math.FA2019★ 1 cited

A q-atomic decomposition of weighted tent spaces on spaces of homogeneous type and its application

Liang Song, Liangchuan Wu

The theory of tent spaces on $R^{n}$ was introduced by Coifman, Meyer and Stein, including atomic decomposition, duality theory and so on. Russ generalized the atomic decomp…

math.AP2019

BMO spaces associated to operators with generalised Poisson bounds on non-doubling manifolds with ends

Peng Chen, Xuan Thinh Duong, Ji Li +2

Consider a non-doubling manifold with ends $M = R^{n} ♯ R^{m}$ where $R^{n} = R^{n} \times S^{m - n}$ for $m > n \geq 3$ . We say that a…

math.AP2019★ 4 cited

Characterizations of the Hardy space $H_{F I O}^{1} (R^{n})$ for Fourier integral operators

Zhijie Fan, Naijia Liu, Jan Rozendaal +1

The Hardy spaces for Fourier integral operators $H_{F I O}^{p} (R^{n})$ , for $1 \leq p \leq \infty$ , were introduced by Smith in [Smith,1998] and Hassell et al. in [H…

math.AP2019

Weak type $(1, 1)$ bounds for Schrödinger groups

Peng Chen, Xuan Thinh Duong, Ji Li +2

Let $L$ be a non-negative self-adjoint operator acting on $L^{2} (X)$ where $X$ is a space of homogeneous type with a dimension $n$ . Suppose that the heat kernel of $L$ satisfies a Ga…

math.AP2019

Frame decomposition and radial maximal semigroup characterization of Hardy spaces associated to operators

Xuan Thinh Duong, Ji Li, Liang Song +1

Let $L$ be the generator of an analytic semigroup whose kernels satisfy Gaussian upper bounds and Hölder's continuity. Also assume that $L$ has a bounded holomorphic functional cal…

math.CA2017

Weighted inequalities of bilinear rough singular integrals

Peng Chen, Danqing He, Liang Song

We establish a quantitative weighted inequality for the bilinear rough singular integral, where the bound is controlled by the cube of the weight constant.

math.AP2017

Carleson measures, BMO spaces and balayages associated to Schrodinger operators

Peng Chen, Xuan Thinh Duong, Ji Li +2

Let $Ł$ be a Schrödinger operator of the form $Ł = - Δ + V$ acting on $L^{2} (R^{n})$ , $n \geq 3$ , where the nonnegative potential $V$ belongs to the reverse Hölder class $B_{q}$ for som…

math.AP2016★ 15 cited

Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity

Jun Geng, Zhongwei Shen, Liang Song

This paper concerns with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We establish uni…

math.AP2016★ 2 cited

Maximal function characterizations for Hardy spaces associated to nonnegative self-adjoint operators on spaces of homogeneous type

Liang Song, Lixin Yan

Let $X$ be a metric measure space with a doubling measure and $L$ be a nonnegative self-adjoint operator acting on $L^{2} (X)$ . Assume that $L$ generates an analytic semigroup $e^{-tL…

math.AP2015

On characterization of Poisson integrals of Schrödinger operators with Morrey traces

Liang Song, Xiaoxiao Tian, Lixin Yan

Let $L$ be a Schrödinger operator of the form $L = - Δ + V$ acting on $L^{2} (R^{n})$ where the nonnegative potential $V$ belongs to the reverse Hölder class $B_{q}$ for some $q\geq n.…

math.AP2015★ 4 cited

A maximal function characterization for Hardy spaces associated to nonnegative self-adjoint operators satisfying Gaussian estimates

Liang Song, Lixin Yan

Let $L$ be a nonnegative, self-adjoint operator satisfying Gaussian estimates on $L^2(\RR^n)$. In this article we give an atomic decomposition for the Hardy spaces $ H^p_{L,max}(\R…

math.AP2014

Preduals of quadratic Campanato spaces associated to operators with heat kernel bounds

Liang Song, Jie Xiao, Xuefang Yan

Let $L$ be a nonnegative, self-adjoint operator on $L^{2} (R^{n})$ with the Gaussian upper bound on its heat kernel. As a generalization of the square Campanato space $\mathcal…

math.AP2013★ 2 cited

On characterization of Poisson integrals of Schrodinger operators with BMO traces

Xuan Thinh Duong, Lixin Yan, Chao Zhang

Let L be a Schrodinger operator of the form L=-Δ+V acting on L^2(Rn) where the nonnegative potential V belongs to the reverse Holder class Bq for some q>= n. Let BMO_L(Rn) denote t…

math.CA2012

The bilinear Bochner-Riesz problem

Frederic Bernicot, Loukas Grafakos, Liang Song +1

Motivated by the problem of spherical summability of products of Fourier series, we study the boundedness of the bilinear Bochner-Riesz multipliers $(1 - ∣ ξ ∣^{2} - ∣ η ∣^{2})_{+}^{δ}$ and we mak…

math.AP2012★ 1 cited

On Lp Estimates in Homogenization of Elliptic Equations of Maxwell's Type

Zhongwei Shen, Liang Song

For a family of second-order elliptic systems of Maxwell's type with rapidly oscillating periodic coefficients in a $C^{1, α}$ domain $Ω$ , we establish uniform estimates of solutio…

math.AP2011★ 2 cited

Uniform W^{1,p} Estimates for Systems of Linear Elasticity in a Periodic Medium

Jun Geng, Zhongwei Shen, Liang Song

Let $L_{ε}$ be a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients. We obtain the uniform $W^{1, p}$ estimate in a Lipschitz dom…

Fefferman--Stein type inequalities via area and maximal functions for Schrödinger operators with applications

The Garnett-Jones Theorem on BMO spaces associated with operators and applications

Dirichlet problem for Schrödinger operators on Heisenberg groups

Pointwise Decay of solutions to the energy critical nonlinear Schrödinger equations

The CMO-Dirichlet problem for the Schrödinger equation in the upper half-space and characterizations of CMO

Lp(R2)-boundedness of Hilbert Transforms and Maximal Functions along Plane Curves with Two-variable Coefficients

A q-atomic decomposition of weighted tent spaces on spaces of homogeneous type and its application

BMO spaces associated to operators with generalised Poisson bounds on non-doubling manifolds with ends

Characterizations of the Hardy space HFIO1​(Rn) for Fourier integral operators

Weak type (1,1) bounds for Schrödinger groups

Frame decomposition and radial maximal semigroup characterization of Hardy spaces associated to operators

Weighted inequalities of bilinear rough singular integrals

Carleson measures, BMO spaces and balayages associated to Schrodinger operators

Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity

Maximal function characterizations for Hardy spaces associated to nonnegative self-adjoint operators on spaces of homogeneous type

On characterization of Poisson integrals of Schrödinger operators with Morrey traces

A maximal function characterization for Hardy spaces associated to nonnegative self-adjoint operators satisfying Gaussian estimates

Preduals of quadratic Campanato spaces associated to operators with heat kernel bounds

On characterization of Poisson integrals of Schrodinger operators with BMO traces

The bilinear Bochner-Riesz problem

On Lp Estimates in Homogenization of Elliptic Equations of Maxwell's Type

Uniform W^{1,p} Estimates for Systems of Linear Elasticity in a Periodic Medium

$L^{p} (R^{2})$ -boundedness of Hilbert Transforms and Maximal Functions along Plane Curves with Two-variable Coefficients

Characterizations of the Hardy space $H_{F I O}^{1} (R^{n})$ for Fourier integral operators

Weak type $(1, 1)$ bounds for Schrödinger groups