Displaying similar documents to “Interpolation of analytic families of operators”

Interpolation between H spaces and non-commutative generalizations (II).

Gilles Pisier (1993)

Revista Matemática Iberoamericana

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We continue an investigation started in a preceding paper. We discuss tha classical result of Carleson connecting Carleson measures with the ∂-equation in a slightly more abstract framework than usual. We also consider a more recent result of Peter Jones which shows the existence of a solution for the ∂-equation, which satisfies simultaneously a good L∞ estimate and a good L1 estimate. This appears as a special case of our main result which can...

Real interpolation for families of Banach spaces

Maria Carro (1994)

Studia Mathematica

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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.

A commutator theorem with applications.

Mario Milman (1993)

Collectanea Mathematica

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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...

On the relation between complex and real methods of interpolation

Mieczysław Mastyło, Vladimir Ovchinnikov (1997)

Studia Mathematica

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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.

Real interpolation and compactness.

Fernando Cobos Díaz (1989)

Revista Matemática de la Universidad Complutense de Madrid

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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.

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

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

Studia Mathematica

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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.

Complex interpolation functors with a family of quasi-power function parameters

Ming Fan (1994)

Studia Mathematica

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For the complex interpolation functors associated with derivatives of analytic functions, the Calderón fundamental inequality is formulated in both additive and multiplicative forms; discretization, reiteration, the Calderón-Lozanovskiĭ construction for Banach lattices, and the Aronszajn-Gagliardo construction concerning minimality and maximality are presented. These more general complex interpolation functors are closely connected with the real and other interpolation functors via function...