an:00021878
Zbl 0748.46038
Stan, I.
On an abstract interpolation method
EN
Lucr. Semin. Mat. Fiz. 1986, No. 1, 37-42 (1986).
00157769
1986
j
46M35
real interpolation methods; \(K\) and \(J\) functionals; rearrangement invariant quasi-norm
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 \textit{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 \textit{I. Stan} and \textit{N. Zopota} [Lucr. Semin. Mat. Fiz. 1984, No. 2, 19-22 (1984; Zbl 0627.46084)].
Zbl 0346.46061; Zbl 0627.46084; Zbl 0546.46061