Interpolation of weighted \(L^1\) spaces---a new proof of the Sedaev-Semenov theorem.
The authors give a new and simplified proof of the theorem of Sedaev-Semenov that the couple \((L^{1}_{w_{0}},L^{1}_{w_{1}})\) of weighted \(L^{1}\) spaces on an arbitrary measure space is a Calderon couple, i.e., all interpolation spaces with respect to this couple can be described in terms of the \(K\)-functional. This is an interesting paper, in the reviewer's opinion, with regard to the methods of the proof and the fact that the norm of the operator \(T\) entering in the statement of theorem does not exceed \(1+\varepsilon\) for any given \(\epsilon>0\).
scientific article; zbMATH DE number 1839952