Yang, Dachun New characterizations of Hajłasz-Sobolev spaces on metric spaces. (English) Zbl 1092.46026 Sci. China, Ser. A 46, No. 5, 675-689 (2003). The author introduces on spaces of homogeneous type \((X, \rho, \mu)\), consisting of a set \(X\), a quasi-metric \(\rho\) and a doubling Borel measure \(\mu\), fractional Sobolev spaces \(W^s_p (X)\) where \(1 \leq p \leq \infty\) and \(s>0\). The paper deals with equivalent characterisations of these spaces in terms of local means and maximal functions. Reviewer: Hans Triebel (Jena) Cited in 59 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 42B35 Function spaces arising in harmonic analysis Keywords:Sobolev space; Lipschitz-type space; embedding theorem; maximal function; space of homogeneous type PDFBibTeX XMLCite \textit{D. Yang}, Sci. China, Ser. A 46, No. 5, 675--689 (2003; Zbl 1092.46026)