Gregory F. LawlerDepartment of Mathematics, Duke UniversityOded SchrammMicrosoft Research, 1, Microsoft Way, Redmond, WA, USAWendelin WernerDépartment de Mathématiques, Université Paris-Sud
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We give a new characterization of the Orlicz–Sobolev space$W$^{1,Ψ}(R^{$n$}) in terms of a pointwise inequality connected to the Young function Ψ. We also study different Poincaré inequalities in the metric measure space.
The sine(hyperbolic)-Gordon hierarchy is shown to be the extension of the modified Korteweg-de Vries (MKdV) hierarchy in the integrodifferential algebra extending the standard differential algebra by means of one antiderivative. The characterization by vanishing residues of the MKdV hierarchy yields the same characterization of the sine(hyperbolic)-Gordon hierarchy in the integrodifferential algebra.
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Chenadec P L. A Survey of Symmetrized and Complete Group Presentations[J]. Advances in Computers, 1993: 135-153.