Tuesday, July 23, 2019 - 10:15 in V4-119
BV and Besov spaces on fractals with Dirichlet forms
A talk in the Oberseminar Geometric Analysis series by
Alexander Teplyaev from University of Connecticut
| 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 work, 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 because it may yield isoperimetric type inequalities and Bounded Variation (BV) function spaces. This is a joint work with Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Luke Rogers, Nageswari Shanmugalingam.
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