LIPSCHITZ - ORLICZ SPACES AND THE LAPLACE EQUATION

STEIN and TAIBLESON gave a characterization for f is an element of L(p )(R(n)) to be in the spaces Lip(alpha, L(p)) and Zyg(alpha, L(p)) in t erms of their Poisson integrals. In this paper we extend their results to Lipschitz-Orlicz spaces Lip(phi, L(M)) and Zygmund-Orlicz spaces Z yg(phi, L(M)) and to the general function phi is an element of P inste ad of the power function phi(t) = t(alpha). Such results describe the behavior of the Laplace equation in terms of the smoothness property o f differences of f in Orlicz spaces L(M)(R(n)). More general spaces La mbda(k)(phi, X, q) are also considered.