Interpolation orbits in couples of spacesOrbites d'interpolation pour les couples d'espaces Lp |
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Authors: | Vladimir I Ovchinnikov |
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Institution: | Voronezh State University, Universitetskaia pl., 1, Voronezh, 394693, Russia |
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Abstract: | We consider linear operators T mapping a couple of weighted Lp spaces {Lp0(U0), Lp1(U1)} into {Lq0(V0),Lq1(V1)} for any 1?p0, p1, q0, q1?∞, and describe the interpolation orbit of any a∈Lp0(U0)+Lp1(U1) that is we describe a space of all {Ta}, where T runs over all linear bounded mappings from {Lp0(U0),Lp1(U1)} into {Lq0(V0),Lq1(V1)}. We show that interpolation orbit is obtained by the Lions–Peetre method of means with functional parameter as well as by the K-method with a weighted Orlicz space as a parameter. To cite this article: V.I. Ovchinnikov, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 881–884. |
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