6 citations · 6 across the 8 of their papers we have counts for
8 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 inequalit…
Radial Sobolev embeddings on spherically symmetric Riemannian manifolds
João Marcos do Ó, Guozhen Lu, Raoní 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}_{+…
Conformally Covariant Boundary Operators and Sharp Higher Order Sobolev Trace Inequalities on Poincaré-Einstein Manifolds
Joshua Flynn, Guozhen Lu, Qiaohua Yang
In this paper we introduce conformally covariant boundary operators for Poincaré-Einstein manifolds satisfying a mild spectral assumption. Using these boundary operators we set up…
Conformally Covariant Boundary Operators and Sharp Higher Order CR Sobolev Trace Inequalities on the Siegel Domain and Complex Ball
Joshua Flynn, Guozhen Lu, Qiaohua Yang
We first introduce an appropriate family of conformally covariant boundary operators associated to the Siegel domain with the Heisenberg group …
Explicit Formulas of Fractional GJMS operators on hyperbolic spaces and sharp fractional Poincaré-Sobolev and Hardy-Sobolev-Maz'ya inequalities
Guozhen Lu, Qiaohua Yang
Using the scattering theory on the hyperbolic space , we give the explicit formulas of the fractional GJMS operators for all $γ\in(0,\frac{n}{2})\setminus\mathb…
Sharp higher order Admas' inequality with exact growth condition on weighted Sobolev spaces
João Marcos do Ó, Guozhen Lu, Raoní Ponciano
This paper introduces a novel higher order Adams inequality that incorporates an exact growth condition for a class of weighted Sobolev spaces. Our rigorous proof confirms the vali…