Geodesic
Interpolation Orbits in Couples of Lebesgue Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 1, pp. 56-68

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The paper deals with interpolation orbits for linear operators acting from an arbitrary couple $\{L_{p_0}(U_0),L_{p_1}(U_1)\}$ of weighted $L_p$ spaces into an arbitrary couple $\{L_{q_0}(V_0),L_{q_1}(V_1)\}$ of such spaces, where $1\le p_0,p_1,q_0, q_1\le\infty$. Here $L_p(U)$ is the space of measurable functions $f$ on a measure space such that $fU\in L_p$, equipped with the norm $\|f\|_{L_p(U)}=\|fU\|_{L_p}$. The paper describes the orbits of arbitrary elements $a\in L_{p_0}(U_0)+L_{p_1}(U_1)$. It contains proofs of the results announced in C. R. Acad. Sci. Paris, Ser. I, 334, 881–884 (2002).
Keywords: space of measurable functions
Mots-clés : interpolation space, interpolation orbit. 
@article{FAA_2005_39_1_a4,
     author = {V. I. Ovchinnikov},
     title = {Interpolation {Orbits} in {Couples} of {Lebesgue} {Spaces}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {56--68},
     publisher = {mathdoc},
     volume = {39},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2005_39_1_a4/}
}
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V. I. Ovchinnikov. Interpolation Orbits in Couples of Lebesgue Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 1, pp. 56-68. http://geodesic.mathdoc.fr/item/FAA_2005_39_1_a4/