A discrete transform and decompositions of distribution spaces

The survey is devoted to the modern state of the theory of interpolation of linear operators acting in Banach spaces. Principal attention is devoted to real and complex methods and applications of the theory of interpolation to analysis.

Interpolation of Linear Operators

The set of multipliers from one vector space to another vector space may be seen as a generalized dual space in the sense of Kothe. We give some properties of this kind of duality and prove precise estimates concerning generalized duality of XP-spaces, Lebesgue, Lorentz, Marcinkiewicz and Orlicz spaces. We complement and unify several previous results of this kind.

Generalized duality of some Banach function spaces

Bilinear interpolation theorems and applications

In this article, the authors study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e.\,g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the $\pm$-method and the Peetre-Gagliardo method, are studied in such a framework. Special emphasize is given to the quasi-Banach case and to the interpolation property.

Interpolation of Morrey-Campanato and Related Smoothness Spaces

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Interpolation of Banach lattices

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Interpolation of Banach lattices