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- Aksoy, A.G., et al.
(författare)
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Lipschitz-Orlicz Spaces and the Laplace Equation
- 1996
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Ingår i: Mathematische Nachrichten. - : Wiley. - 0025-584X .- 1522-2616. ; 178:1, s. 81-101
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Tidskriftsartikel (refereegranskat)abstract
- Stein and Taibleson gave a characterization for f ϵ Lp(ℝn) to be in the spaces Lip (α, Lp) and Zyg(α, Lp) in terms of their Poisson integrals. In this paper we extend their results to Lipschitz-Orlicz spaces Lip (α, Lm) and Zygmund-Orlicz spaces Zyg (φ, 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(φ,X, q) are also considered.
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