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Representation of Banach ideal spaces and factorization of operators
Department of Mathematics, Yaroslavl State University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2005 (English)In: Canadian Journal of Mathematics - Journal Canadien de Mathematiques, ISSN 0008-414X, E-ISSN 1496-2479, Vol. 57, no 5, 897-940 p.Article in journal (Refereed) Published
Abstract [en]

Representation theorems are proved for Banach ideal spaces with the Fatou property which are built by the Calderón-Lozanovskiǐ construction. Factorization theorems for operators in spaces more general than the Lebesgue Lp spaces are investigated. It is natural to extend the Gagliardo theorem on the Schur test and the Rubio de Francia theorem on factorization of the Muckenhoupt Ap weights to reflexive Orlicz spaces. However, it turns out that for the scales far from Lp-spaces this is impossible. For the concrete integral operators it is shown that factorization theorems and the Schur test in some reflexive Orlicz spaces are not valid. Representation theorems for the Calderón-Lozanovskiǐ construction are involved in the proofs

Place, publisher, year, edition, pages
2005. Vol. 57, no 5, 897-940 p.
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URN: urn:nbn:se:ltu:diva-3466Local ID: 14c6afd0-a54a-11db-8975-000ea68e967bOAI: diva2:976324
Validerad; 2005; 20070116 (evan)Available from: 2016-09-29 Created: 2016-09-29Bibliographically approved

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