An inequality in Orlicz function spaces with Orlicz norm

Wang, Jin Cai. "An inequality in Orlicz function spaces with Orlicz norm." Commentationes Mathematicae Universitatis Carolinae 44.3 (2003): 507-514. <http://eudml.org/doc/249151>.

@article{Wang2003,
abstract = {We use Simonenko quantitative indices of an $\mathcal \{N\}$-function $\Phi $ to estimate two parameters $q_\Phi $ and $Q_\Phi $ in Orlicz function spaces $L^\Phi [0,\infty )$ with Orlicz norm, and get the following inequality: $\frac\{B_\Phi \}\{B_\Phi -1\}\le q_\Phi \le Q_\Phi \le \frac\{A_\Phi \}\{A_\phi -1\}$, where $A_\Phi $ and $B_\Phi $ are Simonenko indices. A similar inequality is obtained in $L^\Phi [0,1]$ with Orlicz norm.},
author = {Wang, Jin Cai},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Orlicz spaces; Simonenko indices; $\triangle _2$-condition; Orlicz space; Simonenko index; inequality},
language = {eng},
number = {3},
pages = {507-514},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {An inequality in Orlicz function spaces with Orlicz norm},
url = {http://eudml.org/doc/249151},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Wang, Jin Cai
TI - An inequality in Orlicz function spaces with Orlicz norm
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 3
SP - 507
EP - 514
AB - We use Simonenko quantitative indices of an $\mathcal {N}$-function $\Phi $ to estimate two parameters $q_\Phi $ and $Q_\Phi $ in Orlicz function spaces $L^\Phi [0,\infty )$ with Orlicz norm, and get the following inequality: $\frac{B_\Phi }{B_\Phi -1}\le q_\Phi \le Q_\Phi \le \frac{A_\Phi }{A_\phi -1}$, where $A_\Phi $ and $B_\Phi $ are Simonenko indices. A similar inequality is obtained in $L^\Phi [0,1]$ with Orlicz norm.
LA - eng
KW - Orlicz spaces; Simonenko indices; $\triangle _2$-condition; Orlicz space; Simonenko index; inequality
UR - http://eudml.org/doc/249151
ER -