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Displaying similar documents to “Interpolation methods of means and orbits”

On the relation between complex and real methods of interpolation

Mieczysław Mastyło, Vladimir Ovchinnikov (1997)

Studia Mathematica

Similarity:

We study those compatible couples of Banach spaces for which the complex method interpolation spaces are also described by the K-method of interpolation. As an application we present counter-examples to Cwikel's conjecture that all interpolation spaces of a Banach couple are described by the K-method whenever all complex interpolation spaces have this property.

Lions-Peetre reiteration formulas for triples and their applications

Irina Asekritova, Natan Krugljak, Lech Maligranda, Lyudmila Nikolova, Lars-Erik Persson (2001)

Studia Mathematica

Similarity:

We present, discuss and apply two reiteration theorems for triples of quasi-Banach function lattices. Some interpolation results for block-Lorentz spaces and triples of weighted L p -spaces are proved. By using these results and a wavelet theory approach we calculate (θ,q)-spaces for triples of smooth function spaces (such as Besov spaces, Sobolev spaces, etc.). In contrast to the case of couples, for which even the scale of Besov spaces is not stable under interpolation, for triples we...

On interpolation of tensor products of Banach spaces.

Andreas Defant, Mieczyslaw Mastylo, Carsten Michels (2003)

RACSAM

Similarity:

For the complex interpolation method, Kouba proved an important interpolation formula for tensor products of Banach spaces. We give a partial extension of this formula in the injective case for the Gustavsson?Peetre method of interpolation within the setting of Banach function spaces.

Weak-type operators and the strong fundamental lemma of real interpolation theory

N. Krugljak, Y. Sagher, P. Shvartsman (2005)

Studia Mathematica

Similarity:

We prove an interpolation theorem for weak-type operators. This is closely related to interpolation between weak-type classes. Weak-type classes at the ends of interpolation scales play a similar role to that played by BMO with respect to the L p interpolation scale. We also clarify the roles of some of the parameters appearing in the definition of the weak-type classes. The interpolation theorem follows from a K-functional inequality for the operators, involving the Calderón operator....

Real interpolation and compactness.

Fernando Cobos Díaz (1989)

Revista Matemática de la Universidad Complutense de Madrid

Similarity:

The behavior of compactness under real interpolation real is discussed. Classical results due to Krasnoselskii, Lions-Peetre, Persson, and Hayakawa are described, as well as others obtained very recently by Edmunds, Potter, Fernández, and the author.

A commutator theorem with applications.

Mario Milman (1993)

Collectanea Mathematica

Similarity:

We give an extension of the commutator theorems of Jawerth, Rochberg and Weiss [9] for the real method of interpolation. The results are motivated by recent work by Iwaniek and Sbordone [6] on generalized Hodge decompositions. The main estimates of these authors are based on a commutator theorem for a specific operator acting on Lp spaces and through the use of the complex method of interpolation. In this note we give an extension of the Iwaniek-Sbordone theorem to general real interpolation...