Relations between Kondratiev spaces and refined localization Triebel–Lizorkin spaces

We investigate the close relation between certain weighted Sobolev spaces (Kondratiev spaces) and refined localization spaces from Triebel (2006), Triebel (2008). In particular, using a characterization for refined localization spaces from Scharf (2014), we considerably improve an embedding from Hansen (2013). This embedding is of special interest in connection with convergence rates for adaptive approximation schemes.