Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities
Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities
复制标题
DOI：
10.1016/j.jfa.2020.108459
复制
发表时间：
2018-11
影响因子：
1.7
通讯作者：
Patricia Alonso Ruiz;Fabrice Baudoin;Li Chen;Luke G. Rogers;N. Shanmugalingam;A. Teplyaev
中科院分区：
文献类型：
--
作者：
Patricia Alonso Ruiz;Fabrice Baudoin;Li Chen;Luke G. Rogers;N. Shanmugalingam;A. Teplyaev
我们在狄利克雷空间的一般框架中引入基于热半群的贝索夫类。研究了这些类的一般性质，并获得了该空间尺度中热半群的定量正则化估计。作为本文的一个亮点，我们获得了一个影响深远的 Sobolev 不等式，它是由 N. Varopoulos 在热半群超收缩性假设下证明的。这种情况特别令人感兴趣，因为它产生等周类型不等式。
We introduce heat semigroup-based Besov classes in the general framework of Dirichlet spaces. General properties of those classes are studied and quantitative regularization estimates for the heat semigroup in this scale of spaces are obtained. As a highlight of the paper, we obtain a far reaching-analogue,, of the Sobolev inequality that was proved forby N. Varopoulos under the assumption of ultracontractivity for the heat semigroup. The caseis of special interest since it yields isoperimetric type inequalities.