Sobolev extension domains on metric spaces of homogeneous type.
The author proves that there exists a bounded linear extension operator \[ \text{Ext}: M^{1,p}(\Omega,d,\mu)\to M^{1,p}(\Omega, d,\mu) \] such that \(\text{Ext}(u)|_\Omega= u\), where \(M^{1,p}(\Omega,d,\mu)\) is the Hajlasz space. Here, \((X,d,\mu)\) is a metric measure space of homogeneous type with a finite measure.
scientific article; zbMATH DE number 2083994