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Lipschitz — Orlicz Spaces and the Laplace Equation
Author(s) -
Aksoy A. G.,
Maligranda L.
Publication year - 1996
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19961780104
Subject(s) - mathematics , lipschitz continuity , smoothness , birnbaum–orlicz space , pure mathematics , laplace transform , mathematical analysis , function space , characterization (materials science) , function (biology) , interpolation space , functional analysis , materials science , gene , nanotechnology , evolutionary biology , biology , biochemistry , chemistry
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.