Intrinsic definitions of Besov spaces on domains
by
Sophie Dispa
University of Liège

We study the equivalence between quasi-norms of Besov spaces on domains. These spaces, especially when they are considered on domains, appear to be particularly useful to estimate the quality of approximation of solutions of boundary value problems through numerical methods.

In our work, we suppose that the domain Omega in Rⁿ is bounded and Lipschitz. First, we define Besov spaces on Omega as the restrictions of the corresponding spaces on Rⁿ. Then, using an equivalent and intrinsic (using points of Omega only) Peetre-type characterization of these spaces, we get another equivalent and intrinsic quasi-norm using, this time, generalized differences and moduli of smoothness. This result, which provides a practical formulation in connection with applications to PDE was already known for Besov spaces on C^\infty domains but had still to be proved in the case of Lipschitz domains.

Date received: March 22, 2001