Liang Song

activity

20222026

most citedLocal smoothing and Hardy spaces for Fourier integral operators on manifolds

1 citations · 1 across the 7 of their papers we have counts for

collaborators

9 papers

math.AP2026

Littlewood--Paley operators and semigroup maximal operators on CMO spaces associated to Schödinger operators

Wanjun Li, Qingze Lin, Liang Song

Let $L = - Δ + V$ be a Schrödinger operator on $R^{n}$ , where $Δ$ is the Laplacian and $V$ satisfies the reverse Hölder inequality $RH_{q}$ for some $q > n /2$ . In this paper, w…

math.AP2025

The Hardy spaces $H_{F I O}^{p} (R^{n})$ for Fourier integral operators for $p < 1$

Naijia Liu, Jan Rozendaal, Liang Song

We introduce the Hardy spaces $H_{F I O}^{p} (R^{n})$ for Fourier integral operators for $0 < p < 1$ , thereby extending earlier constructions for $1 \leq p \leq \infty$ .…

math.CA2025

Weak type $(1, 1)$ bounds for Riesz transforms for elliptic operators in non-divergence form

Liang Song, Huohao Zhang

Let $L = - \sum_{i, j = 1}^{n} a_{ij} D_{i} D_{j}$ be the elliptic operator in non-divergence form with smooth real coefficients satisfying uniformly elliptic condition. Let $W$ be the global no…

math.CA2025

$L^{p} \to L^{q}$ estimates for Stein's spherical maximal operators

Naijia Liu, Minxing Shen, Liang Song +1

In this article we consider a modification of the Stein's spherical maximal operator of complex order $α$ on $R^{n}$ : $$ {\mathfrak M}^α_{[1,2]} f(x) =\sup\limits_{t\in [1,…

math.AP2025

$H^{1}$ and $bmo$ regularity for wave equations with rough coefficients

Naijia Liu, Jan Rozendaal, Liang Song

We consider second-order hyperbolic equations with rough time-independent coefficients. Our main result is that such equations are well posed on the Hardy spaces $\mathcal{H}^{s,1}…

math.AP2024

Global solutions to 3D quadratic nonlinear Schrödinger-type equation

Zihua Guo, Naijia Liu, Liang Song

We consider the Cauchy problem to the 3D fractional Schrödinger equation with quadratic interaction of $u u ˉ$ type. We prove the global existence of solutions and scattering pro…

math.CA2024

Spherical maximal functions and Hardy spaces for Fourier integral operators

Abhishek Ghosh, Naijia Liu, Jan Rozendaal +1

We use the Hardy spaces for Fourier integral operators to obtain bounds for spherical maximal functions in $L^{p} (R^{n})$ , $n \geq 2$ , where the radii of the spheres are res…

math.AP2023

Lp bounds for Stein's spherical maximal operators

Naijia Liu, Minxing Shen, Liang Song +1

Let $M^{α}$ be the spherical maximal operators of complex order $α$ on $R^{n}$ . In this article we show that when $n \geq 2$ , suppose \begin{eqnarray*} \|{\frak M}^α f…

math.AP2022★ 1 cited

Local smoothing and Hardy spaces for Fourier integral operators on manifolds

Naijia Liu, Jan Rozendaal, Liang Song +1

We introduce the Hardy spaces for Fourier integral operators on Riemannian manifolds with bounded geometry. We then use these spaces to obtain improved local smoothing estimates fo…

Littlewood--Paley operators and semigroup maximal operators on CMO spaces associated to Schödinger operators

The Hardy spaces HFIOp​(Rn) for Fourier integral operators for p<1

Weak type (1,1) bounds for Riesz transforms for elliptic operators in non-divergence form

Lp→Lq estimates for Stein's spherical maximal operators

H1 and bmo regularity for wave equations with rough coefficients