Real interpolation for families of Banach spaces (II).
María J. Carro (1994)
Collectanea Mathematica
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María J. Carro (1994)
Collectanea Mathematica
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D. Staszak (1992)
Collectanea Mathematica
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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.
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.
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...
Pustylnik, Evgeniy (1996)
Abstract and Applied Analysis
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L. Maligranda, L. E. Persson (1993)
Collectanea Mathematica
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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.
Gunnar Sparr (1978)
Studia Mathematica
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Jan Gustavsson (1982)
Studia Mathematica
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J. I. Bertolo, D. L. Fernandez (1982)
Rendiconti del Seminario Matematico della Università di Padova
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Andreas Defant, Mieczyslaw Mastylo, Carsten Michels (2003)
RACSAM
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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.