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Pointwise multipliers of Calderón-Lozanovskiǐ spaces
Institute of Mathematics of Electric Faculty, Poznań University of Technology.
Institute of Mathematics of Electric Faculty, Poznań University of Technology.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2013 (English)In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 286, no 8-9, 876-907 p.Article in journal (Refereed) Published
Abstract [en]

Several results concerning multipliers of symmetric Banach function spaces are presented firstly. Then the results on multipliers of Calderón-Lozanovskiǐ spaces are proved. We investigate assumptions on a Banach ideal space E and three Young functions φ1, φ2 and φ, generating the corresponding Calderón-Lozanovskiǐ spaces so that the space of multipliers of all measurable x such that x y ∈ Eφ for any can be identified with . Sufficient conditions generalize earlier results by Ando, O'Neil, Zabreǐko-Rutickiǐ, Maligranda-Persson and Maligranda-Nakai. There are also necessary conditions on functions for the embedding to be true, which already in the case when E = L1, that is, for Orlicz spaces give a solution of a problem raised in the book 26. Some properties of a generalized complementary operation on Young functions, defined by Ando, are investigated in order to show how to construct the function φ2 such that . There are also several examples of independent interest.

Place, publisher, year, edition, pages
2013. Vol. 286, no 8-9, 876-907 p.
Research subject
URN: urn:nbn:se:ltu:diva-4610DOI: 10.1002/mana.201100156Local ID: 294ad3d4-3e31-43e3-86ef-a52af5268eb2OAI: diva2:977484
Validerad; 2013; 20130102 (andbra)Available from: 2016-09-29 Created: 2016-09-29Bibliographically approved

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