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

abstract

• 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, $p ge 1$, 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.

authors

• Alonso Ruiz, Patricia

published proceedings

• JOURNAL OF FUNCTIONAL ANALYSIS

author list (cited authors)

• Ruiz, P. A., Baudoin, F., Chen, L. i., Rogers, L. G., Shanmugalingam, N., & Teplyaev, A.

citation count

• 5

complete list of authors

• Ruiz, Patricia Alonso||Baudoin, Fabrice||Chen, Li||Rogers, Luke G||Shanmugalingam, Nageswari||Teplyaev, Alexander

publication date

• June 2020

publisher

• Elsevier  Publisher

published in

• Journal of Functional Analysis  Journal

keywords

• Besov Space
• Dirichlet Space
• Heat Kernel
• Sobolev Inequality

Digital Object Identifier (DOI)

• 10.1016/j.jfa.2020.108459

start page

• 108459

end page

• 108459

volume

• 278

issue

• 11

URL

• http://dx.doi.org/10.1016/j.jfa.2020.108459