On Equivalemce of K- and J-Methods for (n+1)-Tuples of Banach Spaces
1997 (English)In: Studia Mathematica, ISSN 0039-3223, Vol. 122, no 2, 99-116 p.Article in journal (Refereed) Published
It is shown that the main results of the theory of real interpolation, i.e. the equivalence and reiteration theorems, can be extended from couples to a class of (n+1)-tuples of Banach spaces, which includes (n+1)-tuples of Banach function lattices, Sobolev and Besov spaces. As an application of our results, it is shown that Lions' problem on interpolation of subspaces and Semenov's problem on interpolation of subcouples have positive solutions when all spaces are Banach function lattices or their retracts. In general, these problems have negative solutions.
Place, publisher, year, edition, pages
1997. Vol. 122, no 2, 99-116 p.
Interpolation theory, K-functional, J-functional
Research subject Natural Science, Mathematics
IdentifiersURN: urn:nbn:se:liu:diva-106168OAI: oai:DiVA.org:liu-106168DiVA: diva2:714488