Discrete characterisations of Lipschitz spaces on fractals

Abstract

Abstract A. Kamont has discretely characterised Besov spaces on intervals. In this paper, we give a discrete characterisation of Lipschitz spaces on fractals admitting a type of regular sequence of triangulations, and for a class of post critically finite self‐similar sets. This shows that on some fractals, certain discretely defined Besov spaces, introduced by R. Strichartz, coincide with Lipschitz spaces introduced by A. Jonsson and H. Wallin for low order of smoothness. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)