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

Meyries, Martin
Schnaubelt, Roland

facul_11; 01

Date: 02. 03. 2011
Abstract:
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.

Primary MSC: 46E35 Sobolev spaces and other spaces of smooth'' functions, embedding theorems, trace theorems , 46H30 Functional calculus in topological algebras [See also 47A60]
Keywords: Anisotropic fractional Sobolev spaces, polynomial weights, interpolation, embeddings, traces, bounded $\calH^\infty$-calculus, operator sums