Congwen Liu

activity

20172026

most citedTwo classes of integral operators over the Siegel upper half-space

12 citations · 17 across the 15 of their papers we have counts for

collaborators

15 papers

math.CV2026

Compactness and the essential norm on Bergman spaces of the Siegel upper half-space

Peiyao Li, Congwen Liu, Jiajia Si

In this paper, we characterize compactness in terms of the Berezin transform and obtain an essential norm estimate for operators in the Toeplitz algebra on Bergman spaces of the Si…

math.AP2025

CR Yamabe Equation on the Heisenberg Group via the method of moving spheres

Congwen Liu

In this paper, we classify positive solutions to the CR Yamabe equation on the Heisenberg group $H^{n}$ . We show that all such solutions are Jerison-Lee bubbles, without imp…

math.CV2024

A Bloch-type space and the predual of $A_{λ}^{1}$ on the Siegel upper half-space

Congwen Liu, Jiajia Si

This paper aims to determine the predual of the Bergman space $A_{λ}^{1}$ on the Siegel upper half-space. To achieve this, a Bloch-type space $\widetilde{\calB}$ is introduced and stud…

math.AP2023

Lipschitz continuity of the solutions to the Dirichlet problems for the invariant laplacians

Congwen Liu, Heng Xu

This short note is motivated by an attempt to understand the distinction between the Laplace operator and the hyperbolic Laplacian on the unit ball of $R^{n}$ , regarding the…

math.CV2022

A uniqueness property for Bergman functions on the Siegel upper half-space

Congwen Liu, Jiajia Si, Heng Xu

In this paper, we show that the Bergman functions on the Siegel upper half-space enjoy the following uniqueness property: if $f\in A_t^p(\calU)$ and $\bfL^α f\equiv 0$ for some non…

math.FA2020

Toeplitz operators on the unit ball with locally integrable symbols

Raffael Hagger, Congwen Liu, Jari Taskinen +1

We study the boundedness of Toeplitz operators $T_{ψ}$ with locally integrable symbols on weighted harmonic Bergman spaces over the unit ball of $R^{n}$ . Generalizing earlier…

math.AP2020

Schwarz-Pick lemma for harmonic functions

Congwen Liu

Based on the recently proved Khavinson conjecture, we establish an inequality of Schwarz-Pick type for harmonic functions on the unit ball of $R^{n}$ .

math.AP2019★ 1 cited

A proof of the generalized Khavinson conjecture

Congwen Liu

We give a complete proof of the generalized Khavinson conjecture which states that, for bounded harmonic functions on the unit ball of $R^{n}$ , the sharp constants in the es…

math.CV2019★ 1 cited

Positive Toeplitz operators on the Bergman spaces of the Siegel upper half-space

Congwen Liu, Jiajia Si

We characterize bounded and compact positive Toeplitz operators defined on the Bergman spaces over the Siegel upper half-space.

math.CV2018

Weighted integrability of polyharmonic functions in the higher dimensional case

Congwen Liu, Antti Perala, Jiajia Si

This paper is concerned with the $L^{p}$ integrability of $N$ -harmonic functions with respect to the standard weights $(1 - ∣ x ∣^{2})^{α}$ on the unit ball $B$ of $R^{n}$ , $…

math.CV2017★ 1 cited

$L^{p} - L^{q}$ boundedness of Bergman-type operators over the Siegel upper half-space

Congwen Liu, Jiajia Si, Pengyan Hu

We characterize the $L^{p} - L^{q}$ boundedness of Bergman-type operators over the Siegel upper half-space. This extends a recent result of Cheng et. al. (Trans. Amer. Math. Soc. 369:864…

math.CV2017

Weighted Composition Operators Acting on Harmonic Hardy Spaces

Pengyan Hu, Congwen Liu, Taishun Liu +1

Suppose $n \geq 3$ and let $B$ be the open unit ball in $R^{n}$ . Let $φ : B \to B$ be a $C^{2}$ map whose Jacobian does not change sign, and let $ψ$ be a $C^{2}$ function on $B$ . W…

math.CV2017★ 1 cited

Norm estimates for the Bergman and Cauchy-Szegö projections over the Siegel upper half-space

Congwen Liu

We obtain several estimates for the $L^{p}$ operator norms of the Bergman and Cauchy-Szegö projections over the the Siegel upper half-space. As a by-product, we also determine the pr…

math.CV2017★ 1 cited

Two-sided norm estimates for Bergman-type projections with an asymptotically sharp lower bound

Congwen Liu, Antti Perälä, Lifang Zhou

We obtain new two-sided norm estimates for the family of Bergman-type projections arising from the standard weights $(1 - ∣ z ∣^{2})^{α}$ where $α > - 1$ . As $α \to - 1$ , the lower bound is sha…

math.CV2017★ 12 cited

Two classes of integral operators over the Siegel upper half-space

Congwen Liu, Yi Liu, Pengyan Hu +1

We determine exactly when two classes of integral operators are bounded on weighted $L^{p}$ spaces over the Siegel upper half-space.

Compactness and the essential norm on Bergman spaces of the Siegel upper half-space

CR Yamabe Equation on the Heisenberg Group via the method of moving spheres

A Bloch-type space and the predual of Aλ1​ on the Siegel upper half-space

Lipschitz continuity of the solutions to the Dirichlet problems for the invariant laplacians

A uniqueness property for Bergman functions on the Siegel upper half-space

Toeplitz operators on the unit ball with locally integrable symbols

Schwarz-Pick lemma for harmonic functions

A proof of the generalized Khavinson conjecture

Positive Toeplitz operators on the Bergman spaces of the Siegel upper half-space

Weighted integrability of polyharmonic functions in the higher dimensional case

Lp−Lq boundedness of Bergman-type operators over the Siegel upper half-space

Weighted Composition Operators Acting on Harmonic Hardy Spaces

Norm estimates for the Bergman and Cauchy-Szegö projections over the Siegel upper half-space

Two-sided norm estimates for Bergman-type projections with an asymptotically sharp lower bound

Two classes of integral operators over the Siegel upper half-space

A Bloch-type space and the predual of $A_{λ}^{1}$ on the Siegel upper half-space

$L^{p} - L^{q}$ boundedness of Bergman-type operators over the Siegel upper half-space