# zbMATH — the first resource for mathematics

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)].
##### MSC:
 46M35 Abstract interpolation of topological vector spaces