Real interpolation for families of Banach spaces

• Autorzy: Maria J. Carro
• Języki publikacji: EN

Abstrakty

EN

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 $2^N$ spaces and the recent method of Cobos-Peetre.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46M35: Abstract interpolation of topological vector spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 109
• Numer: 1
• Strony: 1-21

Daty

wydano

1994

otrzymano

1992-09-30

poprawiono

1993-05-17

Twórcy

autor

Maria J. Carro

• Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona 08071, Barcelona, Spain.

Bibliografia

• [BL] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin, 1976.
• [C] A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113-190.
• [CP] F. Cobos and J. Peetre, Interpolation of compact operators: the multidimensional case, Proc. London Math. Soc. (3) 63 (1991), 371-400.
• [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.
• [CJ] M. Cwikel and S. Janson, Real and complex interpolation methods for finite and infinite families of Banach spaces, ibid. 66 (1987), 234-290.
• [F] D. L. Fernández, Interpolation of $2^d$ Banach spaces and the Calderón spaces X(E), Proc. London Math. Soc. (3) 56 (1988), 143-162.
• [G] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981.
• [GU] J. Gustavsson, A function parameter in connection with interpolation of Banach spaces, Math. Scand. 42 (1978), 289-305.
• [LP] J. L. Lions et J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math. 19 (1964), 5-68.
• [M] M. Mastyło, The K-functional for a Banach couple $(Ᾱ∂_E_0;K, Ᾱ∂_E_1;K)$, Comment. Math. 25 (1985), 93-108.
• [P] J. Peetre, A theory of interpolation of normed spaces, Lecture notes, Brasilia (Notas de matemática 39, 1968) (1963), 1-86.
• [S] G. Sparr, Interpolation of several Banach spaces, Ann. Mat. Pura Appl. 99 (1974), 247-316.