Lipschitz-Orlicz Spaces and the Laplace Equation

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Mathematics (CMC)

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Stein and Taibleson gave a characterization for f ϵ Lp(ℝn) to be in the spaces Lip (α, Lp) and Zyg, Lp) in terms of their Poisson integrals. In this paper we extend their results to Lipschitz-Orlicz spaces Lip, Lm) and Zygmund-Orlicz spaces Zyg, Lm) and to the general function φ ϵ P instead of the power function φ(t)= tα. Such results describe the behavior of the Laplace equation in terms of the smoothness property of differences of f in Orlicz spaces Lm (IRn). More general spaces δk,X, q) are also considered.

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© 1996 Wiley-VCH Verlag GmbH & Co