Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities

被引：21

作者：

Ruiz, Patricia Alonso ^{[1
]}

Baudoin, Fabrice ^{[3
]}

Chen, Li ^{[3
]}

Rogers, Luke G. ^{[3
]}

Shanmugalingam, Nageswari ^{[2
]}

Teplyaev, Alexander ^{[3
]}

机构：

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[2] Univ Cincinnati, Dept Math Sci, POB 210025, Cincinnati, OH 45221 USA

[3] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2020年 / 278卷 / 11期

基金：

美国国家科学基金会;

关键词：

Besov space; Heat kernel; Dirichlet space; Sobolev inequality; BROWNIAN-MOTION; DISTRIBUTIONS;

D O I：

10.1016/j.jfa.2020.108459

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 L-P-analogue, p >= 1, of the Sobolev inequality that was proved for p = 2 by N. Varopoulos under the assumption of ultracontractivity for the heat semigroup. The case p = 1 is of special interest since it yields isoperimetric type inequalities. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：48

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