Interpolation of weighted \(L^1\) spaces---a new proof of the Sedaev-Semenov theorem.
type: Item
instance of: scholarly article
title: Interpolation of weighted \(L^1\) spaces---a new proof of the Sedaev-Semenov theorem.
zbMATH Open document ID: 1044.46017
author: Michael Cwikel
author: Inna Kozlov
published in: Illinois Journal of Mathematics
publication date: 2003-01-01T00:00:00Z
review text: 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 \(\epsilon>0\).
reviewed by: Nicolae Popa
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 1839952
zbMATH Keywords: Calderon couple
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1839952