The Besov Space B 0,1 1 on Domains

Let be a bounded Lipschitz domain. Define B 0,1 1, r () = {fL 1 (): there is an FB 0,1 1 (n) such that F| = f} and B 0,1 1 z () = {fB 0,1 1 (n) : f = 0 on n\}. In this paper, the authors establish the atomic decompositions of these spaces. As by-products, the authors obtained the regularity on these spaces of the solutions to the Dirichlet problem and the Neumann problem of the Laplace equation of n *.