Hardy spaces and divergence operators on strongly Lipschitz domains of Rn

Let Omega be a strongly Lipschitz domain of R-n. Consider an elliptic second-order divergence operator L (including a boundary condition on partial derivativeOmega) and define a Hardy space by imposing the non-tangential maximal function of the extension of a function f via the Poisson semigroup for L to be in L-1. Under suitable assumptions on L, we identify this maximal Hardy space with H-1(R-n) if Omega = R-n, with H-r(1)(Omega) under the Dirichlet boundary condition, and with H-z(1)(Omega) under the Neumann boundary condition. (C) 2003 Elsevier Science (USA). All rights reserved.