2 citations · 2 across the 8 of their papers we have counts for
9 papers · 1 filter
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…
Optimal stability hierarchies of the Heisenberg Uncertainty Principle for solenoidal fields and of the second order Caffarelli--Kohn--Nirenberg inequalities
Anh Do, Tuan Duong, Nguyen Lam +2
In 2018, V. Maz'ya proposed 75 open problems in analysis and PDEs. One of them is about the best constant for the Heisenberg Uncertainty Principle for solenoidal vector fields moti…
Caffarelli-Kohn-Nirenberg and Weighted Gaussian Poincaré Inequalities: a complete characterization of sharp stability and extensions
Anh Xuan Do, Nguyen Lam, Guozhen Lu +1
We introduce a new family of weighted Gaussian -Poincaré-type inequalities with explicit sharp constants, optimizers, and corresponding sharp -gradient stability estimate…
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…
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…
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…
-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…