On the atomic decomposition for Hardy spaces on Lipschitz domains of $\text{R}{}^{\mathrm{n}}$

Abstract

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