On the relation between complex and real methods of interpolation

 Access to full text

 Full (PDF)

1. [A] S. V. Astashkin, Description of interpolation orbits between $(l_1\left(w_0\right),l_1\left(w_1\right))$ and $(l_{\infty }\left(w_0\right),l_{\infty }\left(w_1\right))$, Mat. Zametki 35 (1984), 497-503 (in Russian); English transl.: Math. Notes 35 (1984), 261-265. 
2. [B] J. Bergh, On the relation between the two complex methods of interpolation, Indiana Univ. Math. J. 28 (1979), 775-778. Zbl0394.41004
3. [BL] J. Bergh and J. Löfström, Interpolation spaces. An Introduction, Springer, Berlin 1976. Zbl0344.46071
4. [BK] Yu. A. Brudnyĭ and N. Ya. Krugljak, Interpolation Functors and Interpolation Spaces. I, North-Holland, Amsterdam, 1991. 
5. [Ca] A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113-190. Zbl0204.13703
6. [Cw1] M. Cwikel, On ${(L_{p}0\left(A_0\right),L_{p}1\left(A_1\right))}_{\theta },q$, Proc. Amer. Math. Soc. 44 (1974), 286-292. 
7. [Cw2] M. Cwikel, Monotonicity properties of interpolation spaces II, Ark. Mat. 19 (1981), 123-136. Zbl0467.46061
8. [Cw3] M. Cwikel, Real and complex interpolation and extrapolation of compact operators, Duke Math. J. 65 (1992), 333-343. Zbl0787.46062
9. [CM1] M. Cwikel and M. Mastyło, The universal right K-property for Banach lattices, preprint. 
10. [CM2] M. Cwikel and M. Mastyło, On Banach couples which satisfy the condition ${(A_0,A_1)}_{\theta },{\infty }^0={(A_0,A_1)}_{\theta },\infty$, preprint. 
11. [CM3] M. Cwikel and M. Mastyło, On interpolation spaces containing copies of $c_0$ and $l_{\infty }$, preprint. 
12. [CN] M. Cwikel and P. Nilsson, On Calderón-Mityagin couples of Banach lattices, in: Proc. Conf. Constructive Theory of Functions, Varna, 1984, Bulgar. Acad. Sci., 1984, 232-236. 
13. [CP] M. Cwikel and J. Peetre, Abstract K and J spaces, J. Math. Pures Appl. 60 (1981), 1-50. 
14. [DKO] V. I. Dmitriev, S. G. Kreĭn and V. I. Ovchinnikov, Fundamentals of the theory of interpolation of linear operators, in: Geometry of Linear Spaces and Operator Theory, Yaroslavl', 1977, 31-74 (in Russian). 
15. [DO] V. I. Dmitriev and V. I. Ovchinnikov, On the real method spaces, Dokl. Akad. Nauk SSSR 246 (1979), 794-799 (in Russian); English transl.: Soviet Math. Dokl. 20 (1979), 538-542. 
16. [H] T. Holmstedt, Interpolation of quasi-normed spaces, Math. Scand. 26 (1970), 177-199. Zbl0193.08801
17. [J] S. Janson, Minimal and maximal methods of interpolation, J. Funct. Anal. 44 (1981), 50-73. Zbl0492.46059
18. [K] N. J. Kalton, Calderón couples of rearrangement invariant spaces, Studia Math. 106 (1993), 233-277. Zbl0810.46020
19. [KPS] S. G. Kreĭn, Yu. I. Petunin and E. M. Semenov, Interpolation of Linear Operators, Nauka, Moscow, 1978 (in Russian); English transl.: Amer. Math. Soc., Providence, 1982. 
20. [M1] M. Mastyło, Interpolation between some symmetric spaces, Arch. Math. (Basel) 52 (1989), 571-579. Zbl0691.46050
21. [M2] M. Mastyło, K-monotone spaces between spaces of absolutely summable series, Forum Math. 2 (1990), 73-87. Zbl0724.46054
22. [MX] M. Mastyło and Q. Xu, Monotonicity between vector-valued bounded sequence spaces, Bull. Polish Acad. Sci. Math. 41 (1993), 177-187. Zbl0805.46076
23. [O1] V. I. Ovchinnikov, Interpolation theorems resulting from Grothendieck's inequality, Funktsional. Anal. i Prilozhen. 10 (4) (1976), 45-54 (in Russian); English transl.: Functional Anal. Appl. 10 (1977), 287-294. 
24. [O2] V. I. Ovchinnikov, The method of orbits in interpolation theory, Math. Rep. 1 (1984), 349-516. 
25. [OD] V. I. Ovchinnikov and V. I. Dmitriev, The limits of the applicability of the K-method of interpolation, in: Collection of Articles on Applications of Functional Analysis, Voronezh 1975, 102-108 (in Russian). 
26. [Pe] J. Peetre, Banach couples, I: Elementary theory, Technical Report, Lund, 1971. 
27. [Pi] G. Pisier, Interpolation between $H^p$ spaces and non-commutative generalizations. I, Pacific J. Math. 155 (1992), 341-368. Zbl0747.46050
28. [R] H. P. Rosenthal, On relatively disjoint families of measures with some applications to Banach space theory, Studia Math. 37 (1970), 13-36. Zbl0227.46027
29. [S] V. A. Shestakov, Complex interpolation in Banach spaces of measurable functions, Vestnik Leningrad. Univ. 19 (1974), 64-68 (in Russian); English transl.: Vestnik Leningrad Univ. Math. 7 (1979). Zbl0297.46028

1. Jesús Bastero, Mario Milman, Francisco Ruiz, On sharp reiteration theorems and weighted norm inequalities