Abstract
The K-functional for a couple of symmetric spaces on (O, ∞) is computed if there is some separation between their fundamental functions.
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References
Arazy, J.: The K-functional of certain pairs of rearrangement invariant spaces. Bull.Austral. Math. Soc. 27,249–257 (1983).
Asekritova, I.U.: On the K-functional of the pair (\(K_{\Phi _0 } (\bar X),K_{\Phi _1 } (\bar X)\)). In: Theory of functions of several real variables, pp.3–32. Jaroslavl' 1980 [Russian].
Bennett, C.: Intermediate spaces and the class Llog+L. Ark. Mat. 11, 215–228 (1973).
Bennett, C.: Estimates for weak-type operators. Bull. Amer. Math. Soc. 79, 933–935 (1973).
Bergh, J.: A generalization of Steffensen's inequality. J. Math. Anal. Appl. 41, 187–191 (1973).
Bergh, J., Löfström, J.: Interpolation spaces. An introduction. Berlin-Heidelberg-New York: Springer 1976.
Brudnyĭ, Ju.A., Krugljak, N.Ja.: Real interpolation functors. Book manuscript. Jaroslavl' 1981 [Russian].
Butzer, P.L., Berens, H.: Semi-groups of operators and approximation. Berlin-Heidelberg-New York: Springer 1967.
Calderón, A.P.: Spaces between L1 and L∞ and the theorem of Marcinkiewicz. Studia Math. 26, 273–299 (1966).
Cwikel, M.: Monotonicity properties of interpolation spaces. Ark. Mat. 14, 213–236 (1976).
Cwikel, M.: K-divisibility of the K-functional and Calderón couples. Ark. Mat. (to appear).
Dmitriev, V.I., Ovčinnikov, V.I.: On interpolation in real method spaces. Dokl. Akad. Nauk SSSR 246, 794–797 (1979) [Russian].
Holmstedt, T.: Interpolation of quasi-normed spaces. Math. Scand. 26, 177–199 (1970).
Krée, P.: Interpolation d'espaces qui ne sont ni normés, ni complets. Applications. Ann. Inst. Fourier 17, 137–174 (1967).
Kreĭ, S.G., Petunin, Ju.I., Semenov, E.M.: Interpolation of linear operators. Trans. Math. Monographs Vol.54. Providence: Amer. Math. Soc. 1982 (Russian edition-Moscow 1978).
Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II, Function spaces. Berlin-Heidelberg-New York: Springer 1979.
Lorentz, G.G., Shimogaki, T.: Interpolation theorems for operators in function spaces. J. Funct. Anal. 2, 31–51 (1968).
Maligranda, L.: A generalization of the Shimogaki theorem. Studia Math. 71, 69–83 (1981).
Maligranda, L.: The K-functional for function spaces. Manuscript. Poznań 1983.
Merucci, C.: Interpolation réelle avec fonction paramètre: réitération et applications aux espaces ∧P (ϕ) (0<p≤+∞). C.R. Acad. Sci. Paris 295, 427–430 (1982).
Milman, M.: Interpolation of operators of mixed weak strong type between rearrangement invariant spaces. Indiana Univ. Math. J. 28, 985–992 (1979).
Milman, M.: The computation of the K functional for couples of rearrangement invariant spaces. Resultate Math. 5, 174–176 (1982).
Nilsson, P.: Reiteration theorems for real interpolation and approximation spaces. Ann. Mat. Pura Appl. 132, 291–330 (1982).
Oklander, E.T. Interpolación, espacios de Lorentz y teorema de Marcinkiewicz. Cursos y seminarios de matemática Fasc. 20, pp. 1–111. Buenos Aires 1965.
Peetre, J.: Nouvelles propriétés d'éspaces d'interpolation. C.R. Acad. Sci. Paris 256, 1242–1246 (1963).
Peetre, J.: Sur le nombre de paramètres dans la définition de certains espaces d'interpolation. Ricerche Mat. 12, 248–261 (1963).
Peetre, J.: A theory of interpolation of normed spaces. Lecture notes, Brasília 1963.
Sagher, Y.: Interpolation of r-Banach spaces. Studia Math. 41, 45–70 (1972).
Sharpley, R.: Spaces Λα(X) and interpolation. J. Func. Anal. 11, 479–513 (1972).
Sharpley, R.: Strong interpolation of Λα(X) and applications. Notices Amer. Math. Soc. 22, 711 (1975).
Torchinsky, A.: The K-functional for rearrangement invariant spaces. Studia Math. 64, 179–190 (1970).
Triebel, H.: Interpolation theory, function spaces, differential operators. Berlin: VEB Deutscher Verlag Wiss. 1978.
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Maligranda, L. (1984). The K-functional for symmetric spaces. In: Cwikel, M., Peetre, J. (eds) Interpolation Spaces and Allied Topics in Analysis. Lecture Notes in Mathematics, vol 1070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099100
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DOI: https://doi.org/10.1007/BFb0099100
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