On some properties of generalized Marcinkiewicz spaces

Evgeniy Pustylnik

Studia Mathematica, Tome 147 (2001), p. 227-243 / Harvested from The Polish Digital Mathematics Library

Résumé

We give a full solution of the following problems concerning the spaces $M_{φ} (X ⃗)$ : (i) to what extent two functions φ and ψ should be different in order to ensure that $M_{φ} (X ⃗) \neq M_{ψ} (X ⃗)$ for any nontrivial Banach couple X⃗; (ii) when an embedding $M_{φ} (X ⃗) ⊊ M_{ψ} (X ⃗)$ can (or cannot) be dense; (iii) which Banach space can be regarded as an $M_{φ} (X ⃗)$ -space for some (unknown beforehand) Banach couple X⃗.

Publié le : 2001-01-01

Zbl 0985.46006

EUDML-ID : urn:eudml:doc:284383

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Evgeniy Pustylnik. On some properties of generalized Marcinkiewicz spaces. Studia Mathematica, Tome 147 (2001) pp. 227-243. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm144-3-3/