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An extension of Bourdaud-Kateb-Meyer theorem

Abstract : Let H be a real separable Hilbert space. We prove that, if 1 < p < infinity and 0 less than or equal to s < 1 + 1/p, then There Exists C > 0, For All f is an element of H-p(s)(H), \\ \f\H \\(Hps) less than or equal to C \\f\\(Hps(H)). The condition s < 1 + 1/p is essential. As a corollary we describe a class of bounded operators on Sobolev space H-p(s) and on Besov space B-p,q(s) for all 1 < p < infinity, 0 < q less than or equal to infinity and 0 less than or equal to s < 1 + 1/p. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
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S Korry. An extension of Bourdaud-Kateb-Meyer theorem. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2000, 331 (3), pp.197--200. ⟨10.1016/S0764-4442(00)01640-2⟩. ⟨hal-00693767⟩

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