Lipschitz — Orlicz Spaces and the Laplace Equation

Stein and Taibleson gave a characterization for f ϵ L p (ℝ n ) to be in the spaces Lip (α, L p ) and Zyg (α , L p ) in terms of their Poisson integrals. In this paper we extend their results to Lipschitz‐Orlicz spaces Lip (α , L m ) and Zygmund‐Orlicz spaces Zyg (φ , L m ) and to the general function φ ϵ P instead of the power function φ( t ) = t α . Such results describe the behavior of the Laplace equation in terms of the smoothness property of differences of f in Orlicz spaces L m (IR n ). More general spaces δ k (φ ,X, q ) are also considered.