Kondratiev spaces of fractional smoothness via refined localization spaces

In this paper, we introduce Kondratiev spaces of fractional smoothness based on their close relation to refined localization spaces. Moreover, we investigate relations to other approaches leading to extensions of the scale of Kondratiev spaces with integer order of smoothness, based on complex interpolation, and give further results for complex interpolation of those function spaces. The results are first established on complements of arbitrary closed Lebesgue null sets and then transferred to domains of polyhedral type. Finally, as an application, we will study Sobolev-type embeddings.