On the atomic decomposition for Hardy spaces on Lipschitz domains of Rn

Let Ω be a special Lipschitz domain on Rn, and L be a second-order elliptic self-adjoint operator in divergence form L=−div(A∇) on Lipschitz domain Ω subject to Neumann boundary condition. In this paper, we give a simple proof of the atomic decomposition for Hardy spaces HNp(Ω) of Ω for a range of p, by means of nontangential maximal function associated with the Poisson semigroup of L.