论文标题
逆转Heisenberg组上的Hardy-Littlewood-Sobolev不平等
Reversed Hardy-Littlewood-Sobolev inequality on Heisenberg group $\mathbb{H}^n$ and CR sphere $\mathbb{S}^{2n+1}$
论文作者
论文摘要
本文主要致力于研究Heisenberg Group $ \ Mathbb {H}^n $和Cr Sphere $ \ MathBB {S}^{2n+1} $的反向的Hardy-Littlewood-Sobolev（HLS）不平等。首先，我们建立了大致逆转的HLS不等式，并为锐利常数提供明确的下限。然后，通过亚临界方法和一些紧凑的技术证明了具有锐利常数的极端函数的存在。我们的方法是不含重排的，可以应用于经典的HLS不平等和其他类似的不平等现象。
This paper is mainly devoted to the study of the reversed Hardy-Littlewood-Sobolev (HLS) inequality on Heisenberg group $\mathbb{H}^n$ and CR sphere $\mathbb{S}^{2n+1}$. First, we establish the roughly reversed HLS inequality and give a explicitly lower bound for the sharp constant. Then, the existence of the extremal functions with sharp constant is proved by subcritical approach and some compactness techniques. Our method is rearrangement free and can be applied to study the classical HLS inequality and other similar inequalities.
