Associate spaces of logarithmic interpolation spaces and generalized Lorentz-Zygmund spaces

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We determine the associate space of the logarithmic interpolation space (X0, X1)1,q,A where X0 and X1 are Banach function spaces over a ?-finite measure space (?, µ). Particularizing the results for the case of the couple (L1, L?) over a non-atomic measure space, we recover results of Opic and Pick on associate spaces of generalized Lorentz-Zygmund spaces L(?,q;A). We also establish the corresponding results for sequence spaces.
[1] C. Bennett and R. Sharpley, “Interpolation of Operators”, Academic Press, Boston, 1988. [2] J. Bergh and J. L¨ofstro¨m, “Interpolation Spaces. An Introduction”, Springer, Berlin, 1976. [3] B.F. Besoy and F. Cobos, Duality for logarithmic interpolation spaces when 0 < q < 1 and applica- tions, J. Math. Anal. Appl. 466 (2018), 373-399. [4] B.F. Besoy, F. Cobos and L.M. Fern´andez-Cabrera, On the structure of a limit class of logarithmic interpolation spaces, preprint, Madrid (2019). [5] F. Cobos and L.M. Fern´andez-Cabrera, The fundamental function of certain interpolation spaces generated by N -tuples of rearrangement-invariant spaces, in “Function Spaces and Inequalities”. Edited by P. Jain and H.-J. Schmeisser, Springer, Singapore, 2017, pp. 1-14. [6] F. Cobos, L.M. Fern´andez-Cabrera and A. Mart´?nez, On a paper of Edmunds and Opic on limiting interpolation of compact operators between Lp spaces, Math. Nachr. 288 (2015) 167-175. [7] F. Cobos and J. Mart´?n, On interpolation of function spaces by methods defined by means of polygons, J. Appox. Theory 132 (2005) 182-203. [8] F. Cobos and A. Segurado, Description of logarithmic interpolation spaces by means of the J. functional and applications, J. Funct. Anal. 268 (2015) 2906-2945. [9] D.E. Edmunds and W.D. Evans, “Hardy Operators, Function Spaces and Embeddings ”, Springer, Berlin, 2004. [10] D.E. Edmunds and B. Opic, Limiting variants of Krasnosel’ski?i’s compact interpolation theorem, J. Funct. Anal. 266 (2014) 3265-3285. [11] W.D. Evans and B. Opic, Real interpolation with logarithmic functors and reiteration, Canad. J. Math. 52 (2000) 920-960. [12] W.D. Evans, B. Opic and L. Pick, Real interpolation with logarithmic functors, J. Inequal. Appl. 7 (2002) 187-269. [13] L. M. Fern´andez-Cabrera, The fundamental function of spaces generated by interpolation methods associated to polygons, Mediterr. J. Math. (2017) 14:17. [14] S.G. Kre?in, Ju.I. Petunin and E.M. Semenov, “Interpolation of Linear Operators”, Amer. Math. Soc., Providence, 1982. [15] P. Meyer-Nieberg, “Banach Lattices”, Springer, Berlin, 1991. [16] B. Opic and L. Pick, On generalized Lorentz-Zygmund spaces, Math. Inequal. Appl. 2 (1999) 391- 467. [17] H. Triebel, “Interpolation Theory, Function Spaces, Differential Operators”, North-Holland, Ams- terdam, 1978. [18] A.C. Zaanen, “Integration”, North-Holland, Amsterdam, 1967.

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