Abstract: We consider the spaces ∧_α of Lipschitz continuous functions on complete Riemannian manifold with nonnegative Ricci curvature. We first give a characeriza-tion of f∈∧_α in terms of its Poisson integral u(x, t), then we show that the Bessel potential J_β mapps ∧_α isomorphically onto ∧_α+β