Interpolation, embeddings and traces of anisotropic fractional Sobolev spaces with temporal weights

We investigate the properties of a class of weighted vector-valued Lp-spaces and the corresponding (an)isotropic Sobolev–Slobodetskii spaces. These spaces arise naturally in the context of maximal Lpregularity for parabolic initial-boundary value problems. Our main tools are operators with a bounded H∞- calculus, interpolation theory, and operator sums. © 2011 Elsevier Inc. All rights reserved