4 papers
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…
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 inequali…
Radial Sobolev embeddings on spherically symmetric Riemannian manifolds
João Marcos do Ã, Guozhen Lu, Raonà Ponciano
We study Sobolev spaces of radial functions on spherically symmetric Riemannian manifolds. Using geodesic polar coordinates, we give a sharp one-dimensional reduction: a radial fun…
Existence and symmetry of extremals for the high order Hardy-Sobolev-Maz'ya inequalities
Guozhen Lu, Chunxia Tao
In this article, we establish the existence of an extremal function for the k-th order critical Hardy-Sobolev-Maz'ya (HSM) inequalities on the upper half space $\mathbb{R}^{n+1}_{+…