论文标题
在BBM-phenomenon上，重量不平等
On the BBM-phenomenon in fractional Poincaré-Sobolev inequalities with weights
论文作者
论文摘要
在本文中，我们统一并改善了布尔加因，布雷兹斯和米洛隆斯的一些结果，以及Fabes，Kenig和Serapioni的加权Poincaré-Sobolev估计。更确切地说，在某些轻微的自然限制下，我们得到了庞加莱 - 索伯夫型不平等的加权对应物，以及分数案例中强壮的类型不平等。 我们获得的结果的一个主要特征是，当分数参数接近$ 1 $时，我们会跟踪所涉及的常数的行为。我们的主要方法是基于来自谐波分析的技术，与广义庞加莱不平等的自我改善特性有关。
In this paper we unify and improve some of the results of Bourgain, Brezis and Mironescu and the weighted Poincaré-Sobolev estimate by Fabes, Kenig and Serapioni. More precisely, we get weighted counterparts of the Poincaré-Sobolev type inequality and also of the Hardy type inequality in the fractional case under some mild natural restrictions. A main feature of the results we obtain is the fact that we keep track of the behaviour of the constants involved when the fractional parameter approaches to $1$. Our main method is based on techniques coming from harmonic analysis related to the self-improving property of generalized Poincaré inequalities.
