Hardy Sobolev spaces on strongly Lipschitz domains of Rn

Secondly, if L=-÷A∇ is a uniformly elliptic second-order divergence operator on Ω with measurable complex coefficients subject to the Dirichlet or the Neumann boundary condition, we compare the norms of L1/2f and ∇f in suitable Hardy spaces on Ω, depending on the boundary condition, under the assumption that the heat kernel of L satisfies suitable estimates.