Publication: The equivalence theorem for logarithmic interpolation spaces in the quasi-Banach case
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2020
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European Mathematical Society
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We study the description by means of the J-functional of logarithmic interpolation spaces (A0, A1) 1, q, A in the category of the p-normed quasi-Banach couples (0 < p ≤ 1). When (A0, A1) is a Banach couple, it is known that the description changes depending on the relationship between q and A. In our more general setting, the parameter p also has an important role as the results show.
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[1] Bennett, G., Some elementary inequalities. Q. J. Math. 38 (1987), 401-425.
[2] Bennett, G., Some elementary inequalities, III. Q. J. Math. 42 (1991), 149-174.
[3] Bennett, C. and Sharpley, R., Interpolation of Operators. Boston: Academic Press 1988.
[4] Bergh, J. and Löfström, J., Interpolation Spaces. An Introduction. Berlin: Springer 1976.
[5] Besoy, B.F. and Cobos, F., Duality for logarithmic interpolation spaces when 0 < q < 1 and applications. J. Math. Anal. Appl. 466 (2018), 373-399.
[6] Besoy, B.F. and Cobos, F., Logarithmic interpolation methods and measure of non-compactness. Quart. J. Math. 00 (2019) 1-23;doi:10.1093/qmathj/haz041.
[7] Besoy, B.F., Cobos, F. and Fernández-Cabrera, L.M., On the structure of a limit class of logarithmic interpolation spaces. Preprint, Madrid (2019).
[8] Brudnyi, Y. and Krugljak, N., Interpolation Functors and Interpolation Spaces Vol. 1. Amsterdam: North-Holland 1991.
[9] Butzer, P.L. and Berens, H., Semi-Groups of Operators and Approximation. Berlin: Springer 1967.
[10] Cobos, F. and Domínguez, O., On Besov spaces of logarithmic smoothness and Lipschitz spaces. J. Math. Anal. Appl. 425 (2015), 71-84.
[11] Cobos, F., Domínguez, O. and Triebel, H., Characterizations of logarithmic Besov spaces in terms of differences, Fourier-analytical decompositions,
wavelets and semi-groups. J. Funct. Anal. 270 (2016), 4386-4425.
[12] Cobos, F., Fernández-Cabrera, L.M., Kühn, T. and Ullrich, T., On an extreme class of real interpolation spaces. J. Funct. Anal. 256 (2009), 2321-2366.
[13] Cobos, F., Fernández-Cabrera, L.M. and Masty lo, M., Abstract limit J-spaces. J. Lond. Math. Soc. 82 (2010), 501-525.
[14] Cobos, F. and Kühn, T., Equivalence of K- and J-methods for limiting real interpolation spaces. J. Funct. Anal. 261 (2011), 3696-3722.
[15] Cobos, F., Kühn, T. and Schonbek, T., One{sided compactness results for Aronszajn-Gagliardo functors. J. Funct. Anal. 106 (1992), 274-313.
[16] Cobos, F. and Segurado, A., Description of logarithmic interpolation spaces by means of the J{functional and applications. J. Funct. Anal. 268 (2015), 2906 -2945.
[17] Cwikel, M. and Peetre, J., Abstract K{ and J{spaces. J. Math. Pures Appl. 60 (1981), 1-50.
[18] Doktorskii, R.Y., Reiteration relations of the real interpolation method. Soviet Math. Dokl. 44 (1992), 665-669.
[19] Edmunds, D.E. and Evans W.D., Hardy Operators, Function Spaces and Embeddings. Berlin: Springer 2004.
[20] Edmunds D.E. and Opic B., Limiting variants of Krasnosel'skii's compact interpolation theorem. J. Funct. Anal. 266 (2014), 3265-3285.
[21] Evans, W.D. and Opic, B., Real interpolation with logarithmic functors and reiteration. Canad. J. Math. 52 (2000), 920-960.
[22] Evans, W.D., Opic, B. and Pick, L., Real interpolation with logarithmic functors. J. Inequal. Appl. 7 (2002), 187-269.
[23] Gustavsson, J., A function parameter in connection with interpolation of Banach spaces. Math. Scand. 42 (1978), 289-305.
[24] Janson, S., Minimal and maximal methods of interpolation. J. Funct. Anal. 44 (1981), 50-73.
[25] König, H., Eigenvalue distributions of compact operators. Basel: Birkhäuser 1986.
[26] Köthe, G., Topological Vector Spaces I. Berlin: Springer 1969.
[27] Nilsson, P., Reiteration theorems for real interpolation and approximation spaces. Ann. Mat. Pura Appl. 132 (1982), 291-330.
[28] Opic, B. and Pick, L., On generalized Lorentz-Zygmund spaces. Math. Inequal. Appl. 2 (1999) 391-467.
[29] Ovchinnikov, V.I., The Method of Orbits in Interpolation Theory. Math. Rep. 1 (1984), 349-515.
[30] Peetre, J., A Theory of Interpolation of Normed Spaces. Notes Mat. 39. Brasilia: Lecture Notes 1963.