Lipschitz — Orlicz Spaces and the Laplace Equation

✍ Scribed by A. G. Aksoy; L. Maligranda

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 771 KB
• Volume: 178
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19961780104

✦ Synopsis

Abstract

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.