摘要
Let Ω be a bounded Lipschitz domain. Define B<sub>1,r</sub><sup>0.1</sup>（Ω）={f∈L<sup>1</sup>（Ω）: there is an F∈ B<sub>1</sub><sup>0.1</sup>（R<sup>n</sup>） such that F|Ω=f| and B<sub>1,z</sub><sup>0.1</sup>（Ω）={f∈B<sub>1</sub><sup>0.1</sup>（R<sup>n</sup>）: f=0 on R<sup>n</sup>\}. 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 on R<sub>+</sub><sup>n</sup>.
Let Ω be a bounded Lipschitz domain. Define B<sub>1,r</sub><sup>0.1</sup>（Ω）={f∈L<sup>1</sup>（Ω）: there is an F∈ B<sub>1</sub><sup>0.1</sup>（R<sup>n</sup>） such that F|Ω=f| and B<sub>1,z</sub><sup>0.1</sup>（Ω）={f∈B<sub>1</sub><sup>0.1</sup>（R<sup>n</sup>）: f=0 on R<sup>n</sup>\}. 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 on R<sub>+</sub><sup>n</sup>.
基金
This research was partially supported by the SEDF
the NNSF of China.
