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Bergh, J. andLöfström, J.,Interpolation spaces. An introduction. (Grundlehren 226.) Springer-Verlag, Berlin-Heidelberg-New York, 1976.
Calderón, A. P., Intermediate spaces and interpolation, the complex method.Studia Math. 24 (1964), 113–190.
Calderón, A. P., Spaces betweenL 1 andL ∞ and the theorem of Marcinkiewicz.Studia Math. 26 (1966), 273–299.
Coifman, R., Cwikel, M., Rochberg, R., Sagher, Y. andWeiss, G. A theory of complex interpolation for families of Banach spaces.Adv. in Math. 43 (1982), 203–209.
Coifman, R., Cwikel, M., Rochberg, R., Sagher, Y. andWeiss, G., Complex interpolation for families of Banach spaces. In:Proceedings of Symposium in Pure Mathematics 35, 2. American Mathematical Society, Providence, 1979.
Gustavsson, J., A function parameter in connection with interpolation of Banach spaces.Math. Scand. 42 (1978), 289–305.
Hardy, G. H., Littlewood, J. E. andPolya, G.,Inequalities. Cambridge University Press,. 1934.
Heinig, H. P., The Marcinkiewicz interpolation theorem extends to weighted spaces.Studia Math. 62 (1978), 163–168.
Hernandez E., Intermediate spaces and the complex method of interpolation for families of Banach spaces.Ann. Scuola Norm. Sup. Pisa, Serie IV,13 (1986), 246–266.
Hernandez, E., A relation between two interpolation methods. In:Interpolation spaces and allied topics. Proceedings, Lund, 1983.Lecture Notes in Mathematics 1070, pp. 80–91. Springer-Verlag, Berlin-Heidelberg-New York, 1985.
Kalugina, T. F., Interpolation of Banach spaces with a functional parameter. The reiteration theorem.Vestnik Moskov Univ., Ser. I, Mat. Mec. 30:6 (1975), 68–77. (English translation:Moscow University, Math. Bull. 30:6 (1975), 108–116.)
Merucci, C., Applications of interpolation with a function parameter to Lorentz, Sobolev and Besov spaces. InInterpolation spaces and allied topics. Proceedings, Lund, 1983. Lecture Notes in Mathematics 1070, pp. 183–201. Springer-Verlag, Berlin-Heidelberg-New York, 1985.
Merucci, C., Interpolation réelle avec function paramètre: reiteration et applications aux spacesΔ p(ϕ)(0<p<∞).C.R. Acad. Sci. Paris, I,295 (1982), 427–430.
Muckenhoupt, B., Hardy's inequality with weights.Studia Math. 44 (1972), 31–38.
O'Neil, R. andWeiss, G., The Hilbert transform and rearrangement of functions.Studia Math. 23 (1963), 189–198.
Sagher, Y., Real interpolation with weights.Indiana Univ. Math. J. 30 (1981), 113–121.
Stein, E. andWeiss, G.,Introduction to Fourier analysis on Euclidean spaces. Princeton University Press, Princeton, 1971.
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The first author was supported by a Fulbright/MEC fellowship and his research was done during a delightful stay at the Mathematical Sciences Research Institute in Berkeley.
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Hernández, E., Soria, J. Spaces of Lorentz type and complex interpolation. Ark. Mat. 29, 203–220 (1991). https://doi.org/10.1007/BF02384337
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DOI: https://doi.org/10.1007/BF02384337