On some properties of generalized Marcinkiewicz spaces
Tom 144 / 2001
Studia Mathematica 144 (2001), 227-243 MSC: Primary 46B20. DOI: 10.4064/sm144-3-3
We give a full solution of the following problems concerning the spaces $M_\varphi ( \vec X )$: (i) to what extent two functions $\varphi $ and $\psi $ should be different in order to ensure that $M_\varphi ( \vec X )\not =M_\psi ( \vec X )$ for any nontrivial Banach couple $ \vec X $; (ii) when an embedding $M_\varphi ( \vec X )\varsubsetneq M_\psi ( \vec X )$ can (or cannot) be dense; (iii) which Banach space can be regarded as an $M_\varphi ( \vec X )$-space for some (unknown beforehand) Banach couple $ \vec X $.