RT Journal Article T1 Duality for logarithmic interpolation spaces when0 < q < 1 and applications A1 Cobos, Fernando A1 Besoy, Blanca F. AB We work with spaces (A0;A1)θ;q;A which are logarithmic perturbations of the real interpolation spaces. We determine the dual of (A0;A1)θ;q;A when0 < q < 1. As we show, if θ = 0 or 1 then the dual space depends on the relationship between q and A. Furthermore we apply the abstract results to compute the dual space of Besov spaces of logarithmic smoothness and the dual space of spaces of compact operators in a Hilbert space which are closeto the Macaev ideals. PB Elsevier SN 1432-0940 YR 2018 FD 2018-06-01 LK https://hdl.handle.net/20.500.14352/12191 UL https://hdl.handle.net/20.500.14352/12191 LA eng NO [1] Almira, J.M., Luther, U.: Compactness and generalized approximation spaces. Numer., Funct. Anal. Optim. 23, 1{38 (2002)[2] Almira, J.M., Luther, U.: Generalized approximation spaces and applications. Math. Nachr. 263, 3{35 (2004)[3] Bingham, N.H., Goldie, C.M., Teugels, J.L.: Regular Variation. Encyclopedia in Mathematics and its Applications, vol. 27, Cambridge Univ. Press, Cambridge (1987)[4] Brudnyi, Ju.A., Krugljak, N.Ja.: About a family of approximation spaces (Russian). In:Theory of functions of several real variables, pp.15-42. Jaroslavl (1978)[5] Butzer, P.L., Scherer, K.: Approximationsprozesse und Interpolationsmethoden. Mannheim, Zürich (1968)[6] Caetano, A.M., Gogatishvili, A., Opic, B.: Sharp embeddings of Besov spaces involving only logarithmic smoothness. J. Approx. Theory 152, 188{214 (2008)[7] Caetano, A.M., Leopold, H.-G.: On generalized Besov and Triebel-Lizorkin spaces of regular distributions. J. Funct. Anal. 264, 2676{2703 (2013)[8] Carl, B., Stephani, I.: Entropy, Compactness and the Approximation of Operators. Cambridge Univ. Press, Cambridge (1990)[9] Cobos, F., Domínguez, O.: Embeddings of Besov spaces of logarithmic smoothness. Studia Math. 223, 193{204 (2014)[10] Cobos, F., Domínguez, O.: Approximation spaces, limiting interpolation and Besovspaces. J. Approx. Theory 189, 43{66 (2015)[11] Cobos, F., Domínguez, O.: On Besov spaces of logarithmic smoothness and Lipschitzspaces. J. Math. Anal. Appl. 425, 71{84 (2015)[12] Cobos, F., Domínguez, O.: On the relationship between two kinds of Besov spaces withsmoothness near zero and some other applications of limiting interpolation. J. FourierAnal. Appl. 22, 1174{1191 (2016)[13] Cobos, F., Domínguez, O., Triebel, H.: Characterizations of logarithmic Besov spacesin terms of di�erences, Fourier-analytical decompositions, wavelets and semi-groups. J. Funct. Anal. 270, 4386{4425 (2016)[14] Cobos, F., K�uhn, T.: Approximation and entropy numbers in Besov spaces of generalized smoothness. J. Approx. Theory 160, 56{70 (2009)[15] Cobos, F., Milman, M.: On a limit class of approximation spaces. Numer. Funct. Anal. Optim. 11, 11{31 (1990)[16] Cobos, F., Resina, I.: Representation theorems for some operator ideals. J. London Math. Soc. 39, 324{334 (1989)[17] Cobos, F., Resina, I.: On some operator ideals de�ned by approximation numbers. In:Geometric Aspects of Banach Spaces, London Math. Soc. Lecture Note Ser., vol. 140, Cambridge Univ. Press, Cambridge (1989), pp. 133-139[18] DeVore, R.A., Lorentz, G.G.: Constructive Approximation. Springer, Berlin (1993)[19] DeVore, R.A., Popov, V.A.: Interpolation of approximation spaces. In: ConstructiveFunction Theory, Bulgarian Academy of Sciences, So�a (1988), pp. 110-119[20] DeVore, R.A., Riemenschneider, S.D., Sharpley, R.C.: Weak interpolation in Banach spaces. J. Funct. Anal. 33, 58{94 (1979)[21] Edmunds, D.E., Evans, W.D.: Hardy Operators, Function Spaces and Embeddings. Springer, Berlin (2004) NO Ministerio de Economía y Competitividad (MINECO) DS Docta Complutense RD 28 abr 2024