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ArticleOriginal scientific text

Title

On equivalence of K- and J-methods for (n+1)-tuples of Banach spaces

Authors 1, 2

Affiliations

  1. Department of Mathematics, Yaroslavl' Pedagogical University, Respublikanskaya 108, 150000, Yaroslavl', Russia
  2. Department of Mathematics, Yaroslavl' State University, Sovetskaya 14, 150000, Yaroslavl', Russia

Abstract

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.

Bibliography

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Studia Mathematica
1997/122/2
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Pages:
99-116
Main language of publication
English
Received
1995-03-27
Accepted
1996-07-08
Published
1997
Exact and natural sciences