Function spaces on fractals
type: Item
instance of: scholarly article
title: Function spaces on fractals
zbMATH Open document ID: 1023.46034
DOI: 10.1016/S0022-1236(02)00035-6
author: Robert S. Strichartz
published in: Journal of Functional Analysis
publication date: 2003-04-28T00:00:00Z
review text: It is the main aim of this paper to introduce on the Sierpinski gasket \(SG\), Hölder-Zygmund spaces \(\Lambda^\alpha (SG)\), (fractional) Sobolev spaces \(L^\alpha_p (SG)\), and Besov spaces \(\Lambda^\alpha_{pq} (SG)\) for all orders of smoothness \(\alpha\) and \(1\leq p \leq \infty\), \(1\leq q \leq \infty\) (in the case of the Besov spaces \(\Lambda^\alpha_{pq} (SG)\) with additional restrictions on the parameters). Embedding, lifting, and interpolation theorems are proved or conjectured. The Hausdorff dimension, the resistance metric and a related Laplacian play a decisive role, but not the natural embedding in the plane. The paper is considered as a first step towards a more comprehensive theory. There are some generalisations to post-critical finite self-similar fractals.
reviewed by: Hans Triebel
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 1901763
zbMATH Keywords: function spaces
zbMATH Keywords: Sierpinski gasket
zbMATH Keywords: fractals
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1901763