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B M O ψ -spaces and applications to extrapolation theory

Stefan Geiss (1997)

Studia Mathematica

We investigate a scale of B M O ψ -spaces defined with the help of certain Lorentz norms. The results are applied to extrapolation techniques concerning operators defined on adapted sequences. Our extrapolation works simultaneously with two operators, starts with B M O ψ - L -estimates, and arrives at L p - L p -estimates, or more generally, at estimates between K-functionals from interpolation theory.

Bases de Schauder dans certains espaces de fonctions holomorphes

Nguyen Thanh Van (1972)

Annales de l'institut Fourier

On étudie les bases de Schauder pour fonctions holomorphes et leurs applications à l’approximation et interpolation.Après avoir établi quelques faits généraux sur les bases et semi-bases, on les applique à l’étude des bases formées par une suite simple de polynômes.L’effort principal est porté sur la preuve de l’existence d’une “bonne” base commune des espaces des fonctions holomorphes sur Ω et χ , où Ω est un domaine de C et χ un compact dans Ω tels que Ω χ soit un domaine régulier pour le problème...

Bilinear operators and limiting real methods

Fernando Cobos, Alba Segurado (2014)

Banach Center Publications

We investigate the behaviour of bilinear operators under limiting real methods. As an application, we show an interpolation formula for spaces of linear operators. Some results on norm estimates for bounded linear operators are also established.

Calderón couples of rearrangement invariant spaces

N. Kalton (1993)

Studia Mathematica

We examine conditions under which a pair of rearrangement invariant function spaces on [0,1] or [0,∞) form a Calderón couple. A very general criterion is developed to determine whether such a pair is a Calderón couple, with numerous applications. We give, for example, a complete classification of those spaces X which form a Calderón couple with L . We specialize our results to Orlicz spaces and are able to give necessary and sufficient conditions on an Orlicz function F so that the pair ( L F , L ) forms a...

Calderon weights and the real interpolation method.

J. Bastero, M. Milman, F. J. Ruiz (1996)

Revista Matemática de la Universidad Complutense de Madrid

We introduce a class of weights for a which a rich theory of real interpolation can be developed. In particular it led us to extend the commutator theorems associated to this method.

Capacitary Orlicz spaces, Calderón products and interpolation

Pilar Silvestre (2014)

Banach Center Publications

These notes are devoted to the analysis on a capacity space, with capacities as substitutes of measures of the Orlicz function spaces. The goal is to study some aspects of the classical theory of Orlicz spaces for these spaces including the classical theory of interpolation.

Characterization of some interpolation spaces (I)

Alessandra Lunardi (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si calcolano alcuni spazi di interpolazione fra spazi di funzioni hölderiane.

Characterization of some interpolation spaces (II)

Alessandra Lunardi (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si caratterizzano alcuni spazi di interpolazione tra spazi di funzioni continue e domini di operatori ellittici del 2° ordine.

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

Ming Fan (1994)

Studia Mathematica

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 parameters...

Distribution and rearrangement estimates of the maximal function and interpolation

Irina Asekritova, Natan Krugljak, Lech Maligranda, Lars-Erik Persson (1997)

Studia Mathematica

There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition. Analogous...

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