Displaying similar documents to “The Lions's problem for Gustavsson-Peetre functor.”

Interpolation properties of a scale of spaces.

A. K. Lerner, L. Liflyand (2003)

Collectanea Mathematica

Similarity:

A scale of function spaces is considered which proved to be of considerable importance in analysis. Interpolation properties of these spaces are studied by means of the real interpolation method. The main result consists in demonstrating that this scale is interpolated in a way different from that for Lp spaces, namely, the interpolation space is not from this scale.

Inequalities and interpolation.

L. Maligranda, L. E. Persson (1993)

Collectanea Mathematica

Similarity:

Some examples of the close interaction between inequalities and interpolation are presented and discussed. An interpolation technique to prove generalized Clarkson inequalities is pointed out. We also discuss and apply to the theory of interpolation the recently found facts that the Gustavsson-Peetre class P can be described by one Carlson type inequality and that the wider class P can be characterized by another Carlson type inequality with blocks.

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

Irina Asekritova, Natan Krugljak (1997)

Studia Mathematica

Similarity:

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...

Interpolation of the measure of non-compactness by the real method

Fernando Cobos, Pedro Fernández-Martínez, Antón Martínez (1999)

Studia Mathematica

Similarity:

We investigate the behaviour of the measure of non-compactness of an operator under real interpolation. Our results refer to general Banach couples. An application to the essential spectral radius of interpolated operators is also given.