Pointwise multipliers of Calderón-Lozanovskiǐ spaces
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
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 Mathematics
IdentifiersURN: urn:nbn:se:ltu:diva-4610DOI: 10.1002/mana.201100156Local ID: 294ad3d4-3e31-43e3-86ef-a52af5268eb2OAI: oai:DiVA.org:ltu-4610DiVA: diva2:977484
Validerad; 2013; 20130102 (andbra)2016-09-292016-09-29Bibliographically approved