On démontre un résultat de dichotomie pour les fonctions qui opèrent sur les restrictions d’algèbres de fonctions holomorphes de plusieurs variables. On obtient ce résultat après étude de la séparation par des fonctions holomorphes de compacts sur certaines hypersurfaces de .
In this paper we define new sequence spaces using the concepts of strong summability and boundedness of index of -th order difference sequences. We establish sufficient conditions for these spaces to reduce to certain spaces of null and bounded sequences.
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 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 forms a...
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.
In this paper we use the Calderón-Zygmund operator theory to prove a Calderón type reproducing formula associated with a para-accretive function. Using our Calderón-type reproducing formula we introduce a new class of the Besov and Triebel-Lizorkin spaces and prove a Tb theorem for these new spaces.
We study sufficient conditions on the weight w, in terms of membership in the classes, for the spline wavelet systems to be unconditional bases of the weighted space . The main tool to obtain these results is a very simple theory of regular Calderón-Zygmund operators.
A Banach space has Pełczyński’s property (V) if for every Banach space every unconditionally converging operator is weakly compact. H. Pfitzner proved that -algebras have Pełczyński’s property (V). In the preprint (Krulišová, (2015)) the author explores possible quantifications of the property (V) and shows that spaces for a compact Hausdorff space enjoy a quantitative version of the property (V). In this paper we generalize this result by quantifying Pfitzner’s theorem. Moreover, we...
For a Banach space X such that all quotients only admit direct decompositions with a number of summands smaller than or equal to n, we show that every operator T on X can be identified with an n × n scalar matrix modulo the strictly cosingular operators SC(X). More precisely, we obtain an algebra isomorphism from the Calkin algebra L(X)/SC(X) onto a subalgebra of the algebra of n × n scalar matrices which is triangularizable when X is indecomposable. From this fact we get some information on the...