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On an abstract interpolation method. (English) Zbl 0748.46038
Summary: We study the real interpolation methods, which are defined with the aid of the \(K\) and \(J\) functionals of J. Peetre. Our methods are denoted by \((f,\rho,K)\) and \((f,\rho,J)\) respectively, where \(\rho\) is a rearrangement invariant quasi-norm on \((0,\infty)\) with respect to the measure \(dt/t\) on \((0,\infty)\) and \(f\) a positive continuous function on \((0,\infty)\). This methods generalise in a natural way the \((f,p,K)\) and \((f,p,J)\) methods introduced by C. Merucci [Interpolation spaces and applied topics in analysis, Proc. Conf., Lund/Swed. 1983, Lect. Notes Math. 1070, 183-201 (1984; Zbl 0546.46061)] and I. Stan and N. Zopota [Lucr. Semin. Mat. Fiz. 1984, No. 2, 19-22 (1984; Zbl 0627.46084)].
46M35 Abstract interpolation of topological vector spaces