5 papers
Sharp weighted Carleman and Huber isoperimetric inequalities on the unit ball in higher dimensions
Zhijie Chen, Changfeng Gui, Shihong Zhang
In this paper, using a limiting approach, we establish a new type of weighted Carleman inequality in all dimensions and classify all extremal functions. In particular, wh…
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…
Classification of solutions to the -flat and constant -curvature equation on the half-space and ball
Xuezhang Chen, Shihong Zhang
For conformal boundary operators associated with the Paneitz operator, we introduce a rigorous definition of the biharmonic Poisson kernel consisting of a pair of kernel functions…
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…
A sharp Sobolev trace inequality of order four on three-balls
Xuezhang Chen, Shihong Zhang
We establish a fourth order sharp Sobolev trace inequality on three-balls, and its equivalence to a third order sharp Sobolev inequality on two-spheres.