Sobolev Spaces on Metric Measure Spaces

Dachun Yang

(School of Mathematical Sciences, Beijing Normal University)

Event: ERC Workshop on Geometric Analysis on sub-Riemannian and Metric Spaces

Date: Oct 13, 2011, time: 08:30

Place: Centro De Giorgi, Scuola Normale Superiore

Abstract. It is well known that the Sobolev spaces play an important role in analysis on metric measure spaces. In this talk, we present some characterizations of Hajlasz-Sobolev spaces on metric measure spaces via grand Littlewood-Paley functions and also the pointwise characterization of Besov spaces, Triebel-Lizorkin spaces, Newton-Besov and Newton-Triebel-Lizorkin spaces on metric measure spaces.