The Besov Space B0,11 on Domains

Let be a bounded Lipschitz domain. Define B0,11,r()=fL1():thereisanFB0,11(Rn)suchthatF|=f and B0,11,z()=fB0,11(Rn):f=0onRn\ifmmode\expandafter\else\expandafter\=\fi. 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 Rn*.