6 papers
Sharp quantitative integral inequalities for general conformally invariant extensions
Qiaohua Yang, Shihong Zhang
In this paper, we develop a refined analysis of hypergeometric functions to establish sharp quantitative integral inequalities for a general family of conformally invariant extensi…
A simple proof of reverse Sobolev inequalities on the sphere and Sobolev trace inequalities on the unit ball
Runmin Gong, Qiaohua Yang, Shihong Zhang
Frank et al. (J. Funct. Anal., 2022) stated that there is no relation between the reversed Hardy-Littlewood-Sobolev (HLS) inequalities and reverse Sobolev inequalities. However, we…
Sharp fractional Sobolev and related inequalities on H-type groups
Yaojun Wang, Qiaohua Yang
We determine the sharp constants for the fractional Sobolev inequalities associated with the conformally invariant fractional powers of the sublaplacian on…
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…