aFriedrich Schiller University Jena, Mathematical Institute, Ernst-Abbe-Platz 3, D-07740, Germany;bHausdorff Centre for Mathematics, Endenicher Allee 60, D-53115 Bonn, Germany
Abstract:
Besov as well as Sobolev spaces of dominating mixed smoothness are shown to be tensor products of Besov and Sobolev spaces defined on R. Using this we derive several useful characterizations from the one-dimensional case to the d-dimensional situation. Finally, consequences for hyperbolic cross approximations, in particular for tensor product splines, are discussed.