RT Journal Article T1 On Interpolation of Function Spaces by Methods Defined by Means of Polygons A1 Cobos, Fernando A1 Martín, Joaquim AB We describe the spaces obtained by applying the interpolation methods associated to polygons toN-tuples of weighted Lp-spaces, N-tuples of classical Lorentz spaces and some other N-tuples offunction spaces. PB Elsevier SN 1096-0430 YR 2005 FD 2005 LK https://hdl.handle.net/20.500.14352/49885 UL https://hdl.handle.net/20.500.14352/49885 LA eng NO [1] I. Asekritova, N. Krugljak, On equivalence of K- and J - methods for (n+1)-tuples of Banach spaces, Studia Math. 122 (1997) 99–116. [2] I. Asekritova, N. Krugljak, L. Maligranda, L. Nikolova, L.-E. Persson, Lions–Peetre reiteration formulas for triples and their applications, Studia Math. 145 (2001) 219–254. [3] C. Bennett, B. Sharpley, Interpolation of Operators, Academic Press, NewYork, 1988. [4] J. Bergh, J. Lofstrom, Interpolation Spaces. An Introduction, Springer, Berlin, 1976. [5] Y. Brudnyıˇ, N. Krugljak, Interpolation functors and interpolation spaces, vol. 1, North-Holland, Amsterdam, 1991. [6] M.J. Carro, L.I. Nikolova, J. Peetre, L.-E. Persson, Some real interpolation methods for families of Banach spaces: a comparison, J. Approx. Theory 89 (1997) 26–57. [7] M.J. Carro, J. Soria,Weighted Lorentz spaces and the Hardy operator, J. Funct. Anal. 112 (1993) 480–494. [8] J. Cerda, H. Coll, J. Martin, Entropy function spaces and interpolation, J. Math. Anal. Appl., accepted. [9] F. Cobos, P. Fernandez–Martinez, Reiteration and a Wolff theorem for interpolation methods defined by means of polygons, Studia Math. 102 (1992) 239–256. [10] F. Cobos, P. Fernandez–Martinez,A duality theorem for interpolation methods associated to polygons, Proc. Amer. Math. Soc. 121 (1994) 1093–1101. [11] F. Cobos, P. Fernandez–Martinez, A. Martinez, On reiteration and the behavior of weak compactness under certain interpolation methods, Collect. Math. 50 (1999) 53–72. [12] F. Cobos, P. Fernandez–Martinez, A. Martinez, Y. Raynaud, On duality between K- and J -spaces, Proc. Edinburgh Math. Soc. 42 (1999) 43–63. [13] F. Cobos, P. Fernandez-Martinez, T. Schonbek, Norm estimates for interpolation methods defined by means of polygons, J. Approx. Theory 80 (1995) 321–351. [14] F. Cobos, T. Kuhn, T. Schonbek, One-sided compactness results for Aronszajn–Gagliardo functors, J. Funct. Anal. 106 (1992) 274–313. [15] F. Cobos, J. Peetre, Interpolation of compact operators: the multidimensional case, Proc. London Math. Soc. 63 (1991) 371–400. [16] M. Cwikel, S. Janson, Real and complex interpolation methods for finite and infinite families of Banach spaces, Adv. Math. 66 (1987) 234–290. [17] S. Ericsson, Certain reiteration and equivalence results for the Cobos–Peetre polygon interpolation method, Math. Scand. 85 (1999) 301–319. [18] A. Favini, Su una estensione del metodo d’interpolazione complesso, Rend. Sem. Mat. Univ. Padova 47 (1972) 243–298. [19] D.L. Fernandez, Interpolation of 2n Banach spaces, Studia Math. 45 (1979) 175–201. [20] D.L. Fernandez, Interpolation of 2d Banach spaces and the Calderon space X(E), Proc. London Math. Soc. 56 (1988) 143–162. [21] C. Foia,s, J.L. Lions, Sur certains theoremes d’interpolation, Acta Sci. Math. (Szeged) 22 (1961) 269–282. [22] S.G. Kreıˇn, Ju.I. Petunin, E.M. Semenov, Interpolation of Linear Operators, American Mathematial Society of Providence, RI, 1982. [23] J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces II, Springer, Verlag, Berlin, Heidelberg, New York, 1979. [24] G.G. Lorentz, On the theory of space _, Pacific J. Math. 1 (1951) 411–429. [25] M. Milman, On interpolation of 2n Banach spaces and Lorentz spaces with mixed norms, J. Funct. Anal. 41 (1981) 1–7. [26] G. Sparr, Interpolation of several Banach spaces, Ann. Math. Pura Appl. 99 (1982) 247–316. [27] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978. [28] A. Yoshikawa, Sur la theorie d’espaces d’interpolation—Les espaces de moyenne de plusieurs espaces de Banach, J. Fac. Sci. Univ. Tokyo 16 (1970) 407–468. NO NATO Collaborative Linkage Grant NO Ministerio de Ciencia y Tecnología NO MCYT Programa Ramón y Cajal , DS Docta Complutense RD 3 may 2024