Interpolation, embeddings and traces of anisotropic fractional Sobolev   spaces with temporal weights
  We investigate the properties of a class of weighted vector-valued $L_p$-spaces and the corresponding (an)isotropic Sobolev-Slobodetskii spaces. These spaces arise naturally in the context of maximal $L_p$-regularity for parabolic initial-boundary value problems. Our main tools are operators with a bounded $\calH^\infty$-calculus, interpolation theory, and operator sums. 
Martin Meyries, Roland Schnaubelt
math.FA