IMASL   20939
INSTITUTO DE MATEMATICA APLICADA DE SAN LUIS "PROF. EZIO MARCHI"
Unidad Ejecutora - UE
artículos
Título:
Maximal Inequalities for a Best Approximation Operator in Orlicz Spaces
Autor/es:
S. FAVIER, F. ZÓ
Revista:
COMMENTATIONES MATHEMATICAE
Editorial:
Polish Mathematical Society
Referencias:
Año: 2011 vol. 51 p. 3 - 21
ISSN:
0010-2628
Resumen:
In this paper we study a maximal operator $mathcal{M} f$ related with the best $ arphi$ approximation by constants for a function $fin L_{loc}^{ arphi ´} ( r^m),$ where we denote by $ arphi ´$ for the derivative function of the $C^1$ convex function $ arphi.$ We get a necessary and sufficient condition which assure strong inequalities of the type $int_{ r^m} heta (mathcal{M} |f|) , dx , le K int_{ r^m} heta ( K |f|) ,dx,$ where $K$ is a constant independent of $f.$ In the particular case $ arphi (t) = t^{p+1}$ we obtain several equivalent conditions on the functions $ heta$ that assures strong inequalities of this type.