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

Patricia Alonso Ruiz, Fabrice Baudoin*, Li Chen, Luke G. Rogers, Nageswari Shanmugalingam, Alexander Teplyaev

*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

21 Citationer (Scopus)

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 Lp-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.

OriginalsprogEngelsk
Artikelnummer108459
TidsskriftJournal of Functional Analysis
Vol/bind278
Nummer11
ISSN0022-1236
DOI
StatusUdgivet - 15 jun. 2020
Udgivet eksterntJa

Fingeraftryk

Dyk ned i forskningsemnerne om 'Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities'. Sammen danner de et unikt fingeraftryk.

Citationsformater