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

Irina Asekritova; Natan Krugljak

Studia Mathematica (1997)

  • Volume: 122, Issue: 2, page 99-116
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Asekritova, Irina, and Krugljak, Natan. "On equivalence of K- and J-methods for (n+1)-tuples of Banach spaces." Studia Mathematica 122.2 (1997): 99-116. <http://eudml.org/doc/216371>.

@article{Asekritova1997,
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.},
author = {Asekritova, Irina, Krugljak, Natan},
journal = {Studia Mathematica},
keywords = {real interpolation; reiteration theorems; Banach function lattices; Sobolev and Besov spaces; Lions' problem; interpolation of subspaces; Semenov's problem},
language = {eng},
number = {2},
pages = {99-116},
title = {On equivalence of K- and J-methods for (n+1)-tuples of Banach spaces},
url = {http://eudml.org/doc/216371},
volume = {122},
year = {1997},
}

TY - JOUR
AU - Asekritova, Irina
AU - Krugljak, Natan
TI - On equivalence of K- and J-methods for (n+1)-tuples of Banach spaces
JO - Studia Mathematica
PY - 1997
VL - 122
IS - 2
SP - 99
EP - 116
AB - 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.
LA - eng
KW - real interpolation; reiteration theorems; Banach function lattices; Sobolev and Besov spaces; Lions' problem; interpolation of subspaces; Semenov's problem
UR - http://eudml.org/doc/216371
ER -

References

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  1. [A1] I. U. Asekritova, On the weak K-divisibility of (n+1)-tuples of ideal Banach spaces, in: Studies in the Theory of Functions of Several Real Variables, Yaroslavl', 1990, 15-21 (in Russian). 
  2. [A2] I. U. Asekritova, A real interpolation method for finite collections of Banach spaces, in: Studies in the Theory of Functions of Several Real Variables, Yaroslavl', 1981, 9-17 (in Russian). 
  3. [A3] I. U. Asekritova, On the property of K-divisibility for finite collections of Banach spaces, in: Studies in the Theory of Functions of Several Real Variables, Yaroslavl', 1984, 3-9 (in Russian). 
  4. [A4] I. U. Asekritova, A counterexample to K-divisibility for (n+1)-tuples of Banach spaces, in: Studies in the Theory of Functions of Several Real Variables, Yaroslavl', 1988, 5-15 (in Russian). 
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