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This is a continuation of our paper "Boundary layer methods for Lipschitz domains in Riemannian manifolds," [MT]. In that paper we have initiated a program aimed at extending the layer potential theory for the flat-space Laplacian on Lipschitz domains in the Euclidean space to the setting of variable coefficients, and more generally to the context of Lipschitz domains in Riemannian manifolds. We recall the general setting, which will also be in effect in this paper. Let M be a smooth, compact Riemannian manifold, of real dimension dimM = n, with a Riemannian metric tensor, which we assume is Lipschitz. That is, M is covered by local coordinate charts in which the components gjk of the metric tensor are Lipschitz functions. (Actually, in [MT] it was assumed that the metric tensor was of class C; we will extend the results of [MT] to the Lipschitz case in §2 of this paper.) Then the Laplace-Beltrami operator on M is given in local coordinates by

Potential theory on Lipschitz domains in Riemannian manifolds: $L^p$ Hardy, and Holder space results