On some properties of generalized Marcinkiewicz spaces

Evgeniy Pustylnik¹

¹ Department of Mathematics Technion - Israel Institute of Technology Haifa 32000, Israel

Studia Mathematica, Tome 144 (2001) no. 3, pp. 227-243

Résumé

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 $.

Détail

DOI : 10.4064/sm144-3-3

Keywords: full solution following problems concerning spaces varphi vec what extent functions varphi psi should different order ensure varphi vec psi vec nontrivial banach couple vec embedding varphi vec varsubsetneq psi vec cannot dense iii which banach space regarded varphi vec space unknown beforehand banach couple vec