Tempered homogeneous function spaces, II

This paper deals with homogeneous function spaces of Besov-Sobolev type within the framework of tempered distributions in Euclidean $n$-space based on Gauss-Weierstrass semi-groups. Related Fourier-analytical descriptions are incorporated afterwards as so-called domestic norms. This approach avoids the usual ambiguity modulo polynomials when homogeneous function spaces are considered in the context of homogeneous tempered distributions. The motivation to deal with these spaces comes from (nonlinear) heat and Navier-Stokes equations, but also from Keller-Segel sytems and other PDE models of chemotaxis.