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Symmetrization, factorization and arithmetic of quasi-Banach function spaces
Institute of Mathematics, Faculty of Electrical Engineering, Poznań University of Technology, Poznań, Poland.
Institute of Mathematics, Faculty of Electrical Engineering, Poznań University of Technology, Poznań, Poland.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0002-9584-4083
2019 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 470, no 2, p. 1136-1166Article in journal (Refereed) Published
Abstract [en]

We investigate relations between symmetrizations of quasi-Banach function spaces and constructions such as Calderón–Lozanovskiĭ spaces, pointwise product spaces and pointwise multipliers. We show that under reasonable assumptions the symmetrization commutates with these operations. We determine also the spaces of pointwise multipliers between Lorentz spaces and Cesàro spaces. The methods that we develop may be regarded as an arithmetic of quasi-Banach function spaces and proofs of Theorem 3, Theorem 4, Theorem 6 give a kind of tutorial for these methods. Finally, the above results will be used in proofs of some factorization results.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 470, no 2, p. 1136-1166
Keywords [en]
Quasi-Banach ideal spaces, Symmetrization operation, Calderón–Lozanovskiĭ spaces, Symmetric spaces, Pointwise products and multipliers, Cesàro spaces
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-71318DOI: 10.1016/j.jmaa.2018.10.054ISI: 000450543200026Scopus ID: 2-s2.0-85055099280OAI: oai:DiVA.org:ltu-71318DiVA, id: diva2:1258172
Note

Validerad;2018;Nivå 2;2018-11-07 (johcin) 

Available from: 2018-10-24 Created: 2018-10-24 Last updated: 2019-01-10Bibliographically approved

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Maligranda, Lech

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