Lipschitz - Orlicz Spaces and the Laplace Equation
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چکیده
STEIN and TAIFJLESON gave a characterization for f E Lp(IRn) to be in the spaces L i p ( a , Lp) and Zyg(a, L p ) in terms of their Poisson integrals. In this paper we extend their results to Lipschitz-Orlicz spaces Lip (cp, L M ) and Zygmund-Orlicz spaces Zyg (cp, L M ) and to the general function cp E P instead of the power function cp(t) = t a . Such results describe the behavior of the Laplace equation in terms of the smoothness property of differences of f in Orlicz spaces L M ( I R ~ ) . More general spaces hk(cp, X, q ) are also considered.
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