We develop a new method of real interpolation for infinite families of Banach spaces that covers the methods of Lions-Peetre, Sparr for N spaces, Fernández for spaces and the recent method of Cobos-Peetre.
@article{bwmeta1.element.bwnjournal-article-smv109i1p1bwm, author = {Maria Carro}, title = {Real interpolation for families of Banach spaces}, journal = {Studia Mathematica}, volume = {108}, year = {1994}, pages = {1-21}, zbl = {0820.46070}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv109i1p1bwm} }
Carro, Maria. Real interpolation for families of Banach spaces. Studia Mathematica, Tome 108 (1994) pp. 1-21. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv109i1p1bwm/
[00000] [BL] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin, 1976. | Zbl 0344.46071
[00001] [C] A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113-190. | Zbl 0204.13703
[00002] [CP] F. Cobos and J. Peetre, Interpolation of compact operators: the multidimensional case, Proc. London Math. Soc. (3) 63 (1991), 371-400. | Zbl 0702.46047
[00003] [CCRSW] R. R. Coifman, M. Cwikel, R. Rochberg, Y. Sagher and G. Weiss, A theory of complex interpolation for families of Banach spaces, Adv. in Math. 43 (1982), 203-229. | Zbl 0501.46065
[00004] [CJ] M. Cwikel and S. Janson, Real and complex interpolation methods for finite and infinite families of Banach spaces, ibid. 66 (1987), 234-290. | Zbl 0646.46070
[00005] [F] D. L. Fernández, Interpolation of Banach spaces and the Calderón spaces X(E), Proc. London Math. Soc. (3) 56 (1988), 143-162. | Zbl 0662.46077
[00006] [G] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981. | Zbl 0469.30024
[00007] [GU] J. Gustavsson, A function parameter in connection with interpolation of Banach spaces, Math. Scand. 42 (1978), 289-305. | Zbl 0389.46024
[00008] [LP] J. L. Lions et J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math. 19 (1964), 5-68.
[00009] [M] M. Mastyło, The K-functional for a Banach couple , Comment. Math. 25 (1985), 93-108.
[00010] [P] J. Peetre, A theory of interpolation of normed spaces, Lecture notes, Brasilia (Notas de matemática 39, 1968) (1963), 1-86.
[00011] [S] G. Sparr, Interpolation of several Banach spaces, Ann. Mat. Pura Appl. 99 (1974), 247-316. | Zbl 0282.46022