New characterizations of Hajłasz-Sobolev spaces on metric spaces
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.
scientific article; zbMATH DE number 5005671