Geodesic
Optimal Banach function space for a given cone of decreasing functions in~a~weighted $L_p$-space
Eurasian mathematical journal, Tome 6 (2015) no. 1, pp. 6-25.

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The problem is considered of constructing optimal (i.e. minimal) generalized Banach function space or optimal Banach function space, containing the given cone of nonnegative, decreasing functions in a weighted Lebesgue space. 
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E. Bakhtigareeva. Optimal Banach function space for a given cone of decreasing functions in~a~weighted $L_p$-space. Eurasian mathematical journal, Tome 6 (2015) no. 1, pp. 6-25. http://geodesic.mathdoc.fr/item/EMJ_2015_6_1_a0/

[1] E. G. Bakhtigareeva, M. L. Goldman, P. P. Zabreiko, “Optimal reconstruction of the generalized Banach function space for given cone of nonnegative functions”, Bulletin of TSU, 19:2 (2014), 316–330 (in Russian)

[2] C. Bennett, R. Sharpley, Interpolation of Operators, Academic, New York, 1988 | MR | Zbl

[3] V. I. Burenkov, M. L. Goldman, “Calculation of the norm of the positive operator on the cone of monotone functions”, Proceedings of the Steklov Institute of Mathematics, 210, 1995, 65–89 (in Russian) | MR | Zbl

[4] M. L. Goldman, P. P. Zabreiko, “Optimal reconstruction of the Banach function space for given cone of nonnegative functions”, Proceedings of the Steklov Institute of Mathematics, 284, 2014, 142–156 (in Russian) | DOI | Zbl

[5] M. L. Goldman, P. P. Zabreiko, “Optimal Banach function space for given cone of nonnegative decreasing functions”, Proceedings of the Institute of Mathematics of Belarus, 22:1 (2014), 24–34 (in Russian)

[6] M. L. Goldman, D. Haroske, “Estimates for continuity envelopes and approximation numbers of Bessel potentials”, Journal of Approximation Theory, 172 (2013), 58–85 | DOI | MR | Zbl

[7] S. G. Krein, Yu. I. Petunin, E. M. Semenov, Interpolation of linear operators, Science, M., 1978 (in Russian) | MR

[8] E. Sawyer, “Boundedness of classical operators on classical Lorentz spaces”, Studia Math., 96 (1990), 145–158 | MR | Zbl

[9] P. P. Zabreiko, “Nonlinear integral operators”, Proceedings of the seminar on functional analysis, 8, Voronezh, 1966, 3–148 (in Russian) | MR