8 citations · 23 across the 15 of their papers we have counts for
18 papers
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 , and consequently they allow us to derive th…
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 with the…
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 -Caffa…
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 -dimensional submanifold of a complete noncompact Riemannian manifold with nonnegative sectional curvature. Th…
Sharp -stability and gradient stability hierarchies of the -Poincaré inequalities on Euclidean balls and Gaussian Poincaré inequality
Nguyen Lam, Guozhen Lu
We study the sharp -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…
Sharp -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 -Caffarelli--Kohn--Nirenberg (CKN) inequalities have been extensively studied in the entire Euclidean spaces, the corresponding problem on domains whose bou…
Logarithmic Sobolev, Poincaré and Beckner Inequalities on Hyperbolic Spaces and Riemannian Manifolds
Anh Xuan Do, Debdip Ganguly, Nguyen Lam +1
We investigate several functional and geometric inequalities on the hyperbolic space , with a primary emphasis on logarithmic Sobolev inequalities, Poincaré inequalit…
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…
-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…
-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 -Hardy identities and the -Caffarelli-Kohn-Nirenberg identities (Theorems 1.3 and 1.4) and …
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…
Caffarelli-Kohn-Nirenberg identities, inequalities and their stabilities
Cristian Cazacu, Joshua Flynn, Nguyen Lam +1
We set up a one-parameter family of inequalities that contains both the Hardy inequalities (when the parameter is 1) and the Caffarelli-Kohn-Nirenberg inequalities (when the parame…
Hardy inequalities for magnetic -Laplacians
Cristian Cazacu, David Krejcirik, Nguyen Lam +1
We establish improved Hardy inequalities for the magnetic -Laplacian due to adding nontrivial magnetic fields. We also prove that for Aharonov-Bohm magnetic fields the sharp con…
Caffarelli-Kohn-Nirenberg inequalities for curl-free vector fields and second order derivatives
Cristian Cazacu, Joshua Flynn, Nguyen Lam
The present work has as a first goal to extend the previous results in \cite{CFL20} to weighted uncertainty principles with nontrivial radially symmetric weights applied to curl-fr…
Short proofs of refined sharp Caffarelli-Kohn-Nirenberg inequalities
Cristian Cazacu, Joshua Flynn, Nguyen Lam
This note relies mainly on a refined version of the main results of the paper by F. Catrina and D. Costa (J. Differential Equations 2009). We provide very short and self-contained…
Sharp constants and optimizers for a class of the Caffarelli-Kohn-Nirenberg inequalities
Nguyen Lam, Guozhen Lu
In this paper, we will use a suitable tranform to investigate the sharp constants and optimizers for the following Caffarelli-Kohn-Nirenberg inequalities for a wide range of parame…
Sharp singular Adams inequalities in high order Sobolev spaces
Nguyen Lam, Guozhen Lu
In this paper, we prove a version of weighted inequalities of exponential type for fractional integrals with sharp constants in any domain of finite measure in . Us…
Sharp Adams type inequalities in Sobolev spaces for arbitrary integer
Nguyen Lam, Guozhen Lu
The main purpose of our paper is to prove sharp Adams-type inequalities in unbounded domains of for the Sobolev space $W^{m,\frac{n}{m}}\left(\mathbb{R} ^{n}\right…