Displaying similar documents to “On interpolation of weighted L p -spaces and Ovchinnikov’s theorem”

Inequalities and interpolation.

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

Collectanea Mathematica


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.

The Lions's problem for Gustavsson-Peetre functor.

E.I. Bereznoi, Mieczyslaw Mastylo (1990)

Publicacions Matemàtiques


The problem of coincidence of the interpolation spaces obtained by use of the interpolation method of Gustavsson-Peetre generated by (parameters) quasi-concave functions is investigated. It is shown that a restriction of this method to the class of all non-trivial Banach couples gives different interpolation spaces whenever two different parameters satisfying some conditions are used.

Real interpolation for families of Banach spaces

Maria Carro (1994)

Studia Mathematica


We develop a new method of real interpolation for infinite families of Banach spaces that covers the methods of Lions-Peetre, Sparr for N spaces, Fernández for 2 N spaces and the recent method of Cobos-Peetre.

On the relation between complex and real methods of interpolation

Mieczysław Mastyło, Vladimir Ovchinnikov (1997)

Studia Mathematica


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.

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

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

Studia Mathematica


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.

Real interpolation and compactness.

Fernando Cobos Díaz (1989)

Revista Matemática de la Universidad Complutense de Madrid


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.