5 papers
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…
Heisenberg Uncertainty Principle on half spaces and Orthants: Best constants, Optimizers and Stability
Nguyen Lam, Yukta Lodha, Guozhen Lu +1
Though the sharp Heisenberg Uncertainty Principle has been extensively studied in the entire Euclidean spaces, the counterpart on the half spaces or more general orthants has been…
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 -calculus to establish the Poincaré inequality with monomial Gaussian measure, and then apply the duality approach to st…
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…