On some properties of generalized Marcinkiewicz spaces

Evgeniy Pustylnik. "On some properties of generalized Marcinkiewicz spaces." Studia Mathematica 144.3 (2001): 227-243. <http://eudml.org/doc/284383>.

@article{EvgeniyPustylnik2001,
abstract = {We give a full solution of the following problems concerning the spaces $M_\{φ\}(X⃗)$: (i) to what extent two functions φ and ψ should be different in order to ensure that $M_\{φ\}(X⃗) ≠ M_\{ψ\}(X⃗)$ for any nontrivial Banach couple X⃗; (ii) when an embedding $M_\{φ\}(X⃗) ⊊ M_\{ψ\}(X⃗)$ can (or cannot) be dense; (iii) which Banach space can be regarded as an $M_\{φ\}(X⃗)$-space for some (unknown beforehand) Banach couple X⃗.},
author = {Evgeniy Pustylnik},
journal = {Studia Mathematica},
keywords = {generalized Marcinkiewicz spaces; interpolation; Peetre’s -functional},
language = {eng},
number = {3},
pages = {227-243},
title = {On some properties of generalized Marcinkiewicz spaces},
url = {http://eudml.org/doc/284383},
volume = {144},
year = {2001},
}

TY - JOUR
AU - Evgeniy Pustylnik
TI - On some properties of generalized Marcinkiewicz spaces
JO - Studia Mathematica
PY - 2001
VL - 144
IS - 3
SP - 227
EP - 243
AB - We give a full solution of the following problems concerning the spaces $M_{φ}(X⃗)$: (i) to what extent two functions φ and ψ should be different in order to ensure that $M_{φ}(X⃗) ≠ M_{ψ}(X⃗)$ for any nontrivial Banach couple X⃗; (ii) when an embedding $M_{φ}(X⃗) ⊊ M_{ψ}(X⃗)$ can (or cannot) be dense; (iii) which Banach space can be regarded as an $M_{φ}(X⃗)$-space for some (unknown beforehand) Banach couple X⃗.
LA - eng
KW - generalized Marcinkiewicz spaces; interpolation; Peetre’s -functional
UR - http://eudml.org/doc/284383
ER -