Relations between weighted Orlicz and $BM{O}_{\phi }$ spaces through fractional integrals

Harboure, Eleonor Ofelia, Salinas, Oscar, and Viviani, Beatriz E.. "Relations between weighted Orlicz and $BMO_\phi $ spaces through fractional integrals." Commentationes Mathematicae Universitatis Carolinae 40.1 (1999): 53-69. <http://eudml.org/doc/248439>.

@article{Harboure1999,
abstract = {We characterize the class of weights, invariant under dilations, for which a modified fractional integral operator $I_\alpha $ maps weak weighted Orlicz$-\phi $ spaces into appropriate weighted versions of the spaces $BMO_\psi $, where $\psi (t)=t^\{\alpha /n\}\phi ^\{-1\}(1/t)$. This generalizes known results about boundedness of $I_\alpha $ from weak $L^p$ into Lipschitz spaces for $p>n/\alpha $ and from weak $L^\{n/\alpha \}$ into $BMO$. It turns out that the class of weights corresponding to $I_\alpha $ acting on weak$-L_\phi $ for $\phi $ of lower type equal or greater than $n/\alpha $, is the same as the one solving the problem for weak$-L^p$ with $p$ the lower index of Orlicz-Maligranda of $\phi $, namely $\omega ^\{p^\{\prime \}\}$ belongs to the $A_1$ class of Muckenhoupt.},
author = {Harboure, Eleonor Ofelia, Salinas, Oscar, Viviani, Beatriz E.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {theory of weights; Orlicz spaces; $BMO$ spaces; fractional integrals; theory of weights; Orlicz spaces; BMO spaces; fractional integrals},
language = {eng},
number = {1},
pages = {53-69},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Relations between weighted Orlicz and $BMO_\phi $ spaces through fractional integrals},
url = {http://eudml.org/doc/248439},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Harboure, Eleonor Ofelia
AU - Salinas, Oscar
AU - Viviani, Beatriz E.
TI - Relations between weighted Orlicz and $BMO_\phi $ spaces through fractional integrals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 1
SP - 53
EP - 69
AB - We characterize the class of weights, invariant under dilations, for which a modified fractional integral operator $I_\alpha $ maps weak weighted Orlicz$-\phi $ spaces into appropriate weighted versions of the spaces $BMO_\psi $, where $\psi (t)=t^{\alpha /n}\phi ^{-1}(1/t)$. This generalizes known results about boundedness of $I_\alpha $ from weak $L^p$ into Lipschitz spaces for $p>n/\alpha $ and from weak $L^{n/\alpha }$ into $BMO$. It turns out that the class of weights corresponding to $I_\alpha $ acting on weak$-L_\phi $ for $\phi $ of lower type equal or greater than $n/\alpha $, is the same as the one solving the problem for weak$-L^p$ with $p$ the lower index of Orlicz-Maligranda of $\phi $, namely $\omega ^{p^{\prime }}$ belongs to the $A_1$ class of Muckenhoupt.
LA - eng
KW - theory of weights; Orlicz spaces; $BMO$ spaces; fractional integrals; theory of weights; Orlicz spaces; BMO spaces; fractional integrals
UR - http://eudml.org/doc/248439
ER -