Guozhen Lu

activity

20232026

most cited

L^{p}

-Caffarelli-Kohn-Nirenberg inequalities and their stabilities

2 citations · 2 across the 12 of their papers we have counts for

collaborators

15 papers

math.AP2026

The stability of Sharp Poincaré and Brascamp--Lieb inequalities with full monomial weights

Nguyen Lam, Guozhen Lu, Andrey Russanov

It was known that the Gaussian measures with monomial weights satisfy the sharp pointwise curvature-dimension condition $C D (1, \infty)$ , and consequently they allow us to derive th…

math.AP2026

Sharp uniform stability of the logarithmic Sobolev inequality on finite cycles and stability of the cubic Sobolev inequality

Lu Chen, Nguyen Lam, Guozhen Lu

We determine the sharp uniform constant in the quartic stability estimate for the logarithmic Sobolev inequality on finite cycles. We equip $C_{n} = Z / n Z$ with the…

math.AP2026

A Fourier approach to the sharp stability of Heisenberg Uncertainty Principles of higher and fractional orders: a new perspective

Anh Do, Nguyen Lam, Guozhen Lu +1

We show that, on the Fourier side, the sharp second order Heisenberg Uncertainty Principle (HUP) and its sharp stability for functions are nothing but the first order $L^{2}$ -Caffa…

math.DG2026

Pólya--Szegö Inequality on Submanifolds of Riemannian Manifolds with Nonnegative Curvature and Applications

Anh Xuan Do, Nguyen Lam, Guozhen Lu +1

We prove a Pólya--Szegö inequality for functions defined on an $n$ -dimensional submanifold $Σ$ of a complete noncompact Riemannian manifold with nonnegative sectional curvature. Th…

math.AP2026

Sharp $L^{2}$ -stability and gradient stability hierarchies of the $L^{2}$ -Poincaré inequalities on Euclidean balls and Gaussian Poincaré inequality

Nguyen Lam, Guozhen Lu

We study the sharp $L^{2}$ -Poincaré inequalities on Euclidean balls and with respect to the Gaussian measure, and we focus on their stability. In both settings, the sharp constant is…

math.AP2026

Sharp $L^{2}$ -Caffarelli--Kohn--Nirenberg and weighted Poincaré inequalities on half-spaces and orthants and their stability

Nguyen Lam, Yukta Lodha, Guozhen Lu +1

Though the sharp $L^{2}$ -Caffarelli--Kohn--Nirenberg (CKN) inequalities have been extensively studied in the entire Euclidean spaces, the corresponding problem on domains whose bou…

math.AP2026

Caffarelli-Kohn-Nirenberg and Weighted Gaussian Poincaré Inequalities: a complete characterization of sharp $L^{2}$ stability and $L^{p}$ extensions

Anh Xuan Do, Nguyen Lam, Guozhen Lu +1

We introduce a new family of weighted Gaussian $L^{2}$ -Poincaré-type inequalities with explicit sharp constants, optimizers, and corresponding sharp $L^{2}$ -gradient stability estimate…

math.FA2026

Log-Sobolev and Beckner inequalities and stability of Poincaré inequality with weighted Gaussian measures

Nguyen Lam, Guozhen Lu, Andrey Russanov

We employ a Markov semigroup approach combined with the $Γ$ -calculus to establish a generalized Beckner inequality associated with weighted Gaussian measures. As a direct consequen…

math.AP2025

Sharp stability of the Heisenberg Uncertainty Principle: Second-Order and Curl-Free Field Cases

Anh Xuan Do, Nguyen Lam, Guozhen Lu

Using techniques from harmonic analysis, we derive several sharp stability estimates for the second order Heisenberg Uncertainty Principle. We also present the explicit lower and u…

math.AP2025

Stability of Gaussian Poincaré inequalities and Heisenberg Uncertainty Principle with monimial weights

Nguyen Lam, Guozhen Lu, Andrey Russanov

We use the Bakry-Émery curvature-dimension criterion and $Γ$ -calculus to establish the Poincaré inequality with monomial Gaussian measure, and then apply the duality approach to st…

math.AP2024

Sobolev interpolation inequalities with optimal Hardy-Rellich inequalities and critical exponents

Nguyen Anh Dao, Anh Xuan Do, Nguyen Lam +1

We establish a new family of the critical higher order Sobolev interpolation inequalities for radial functions as well as for non-radial functions. These Sobolev interpolation ineq…

math.AP2024

Scale-Dependent Poincaré inequalities, log-Sobolev inequality and the stability of the Heisenberg Uncertainty Principle on the hyperbolic space

Anh Xuan Do, Debdip Ganguly, Nguyen Lam +1

We establish a general scale-dependent Poincaré-Hardy type identity involving a vector field on the hyperbolic space. By choosing suitable parameter, potential and vector field in…

math.AP2023

$L^{p}$ -Hardy identities and inequalities with respect to the distance and mean distance to the boundary

Joshua Flynn, Nguyen Lam, Guozhen Lu

Firstly, this paper establishes useful forms of the remainder term of Hardy-type inequalities on general domains where the weights are functions of the distance to the boundary. Fo…

math.AP2023★ 2 cited

$L^{p}$ -Caffarelli-Kohn-Nirenberg inequalities and their stabilities

Anh Xuan Do, Joshua Flynn, Nguyen Lam +1

We establish a general identity (Theorem 1.2) that implies both the $L^{p}$ -Hardy identities and the $L^{p}$ -Caffarelli-Kohn-Nirenberg identities (Theorems 1.3 and 1.4) and $L^{p}$ …

math.AP2023

A new approach to weighted Hardy-Rellich inequalities: improvements, symmetrization principle and symmetry breaking

Anh Xuan Do, Nguyen Lam, Guozhen Lu

We investigate necessary and sufficient conditions on the weights for the Hardy-Rellich inequalities to hold, and propose a new way to use the notion of Bessel pair to establish th…

The stability of Sharp Poincaré and Brascamp--Lieb inequalities with full monomial weights

Sharp uniform stability of the logarithmic Sobolev inequality on finite cycles and stability of the cubic Sobolev inequality

A Fourier approach to the sharp stability of Heisenberg Uncertainty Principles of higher and fractional orders: a new perspective

Pólya--Szegö Inequality on Submanifolds of Riemannian Manifolds with Nonnegative Curvature and Applications

Sharp L2-stability and gradient stability hierarchies of the L2-Poincaré inequalities on Euclidean balls and Gaussian Poincaré inequality

Sharp L2-Caffarelli--Kohn--Nirenberg and weighted Poincaré inequalities on half-spaces and orthants and their stability

Caffarelli-Kohn-Nirenberg and Weighted Gaussian Poincaré Inequalities: a complete characterization of sharp L2 stability and Lp extensions

Log-Sobolev and Beckner inequalities and stability of Poincaré inequality with weighted Gaussian measures

Sharp stability of the Heisenberg Uncertainty Principle: Second-Order and Curl-Free Field Cases

Stability of Gaussian Poincaré inequalities and Heisenberg Uncertainty Principle with monimial weights

Sobolev interpolation inequalities with optimal Hardy-Rellich inequalities and critical exponents

Scale-Dependent Poincaré inequalities, log-Sobolev inequality and the stability of the Heisenberg Uncertainty Principle on the hyperbolic space

Lp-Hardy identities and inequalities with respect to the distance and mean distance to the boundary

Lp-Caffarelli-Kohn-Nirenberg inequalities and their stabilities

A new approach to weighted Hardy-Rellich inequalities: improvements, symmetrization principle and symmetry breaking

Sharp $L^{2}$ -stability and gradient stability hierarchies of the $L^{2}$ -Poincaré inequalities on Euclidean balls and Gaussian Poincaré inequality

Sharp $L^{2}$ -Caffarelli--Kohn--Nirenberg and weighted Poincaré inequalities on half-spaces and orthants and their stability

Caffarelli-Kohn-Nirenberg and Weighted Gaussian Poincaré Inequalities: a complete characterization of sharp $L^{2}$ stability and $L^{p}$ extensions

$L^{p}$ -Hardy identities and inequalities with respect to the distance and mean distance to the boundary

$L^{p}$ -Caffarelli-Kohn-Nirenberg inequalities and their stabilities