Interpolation orbits in couples of 𝐋 𝐩 spaces
Comptes Rendus. Mathématique, Volume 334 (2002) no. 10, pp. 881-884.

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 aLp0(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.

Nous considérons les opérateurs T partant d'un couple d'espaces Lp à poids {Lp0(U0), Lp1(U1)} à valeurs dans {Lq0(V0),Lq1(V1)}, où 1⩽p0, p1, q0, q1⩽∞, et donnons une description de l'orbite d'interpolation de tout élément aLp0(U0)+Lp1(U1) ; autrement dit nous décrivons l'espace de toutes les images {Ta}, où T parcourt l'espace des opérateurs linéaires bornés de {Lp0(U0),Lp1(U1)} dans {Lq0(V0),Lq1(V1)}. Nous montrons que l'orbite d'interpolation est obtenue par la méthode des moyennes de Lions–Peetre avec un paramètre fonctionnel, et aussi par la K-méthode avec un espace d'Orlicz à poids comme paramètre fonctionnel.

Received:
Accepted:
DOI: 10.1016/S1631-073X(02)02351-8
Ovchinnikov 1

1 Voronezh State University, Universitetskaia pl., 1, Voronezh, 394693, Russia
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Ovchinnikov. Interpolation orbits in couples of $ \mathbf{L}_{\mathbf{p}}$ spaces. Comptes Rendus. Mathématique, Volume 334 (2002) no. 10, pp. 881-884. doi : 10.1016/S1631-073X(02)02351-8. http://www.numdam.org/articles/10.1016/S1631-073X(02)02351-8/

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