Relations between weighted Orlicz and $BMO_\phi$ spaces through fractional integrals
Harboure, Eleonor Ofelia ; Salinas, Oscar ; Viviani, Beatriz E.
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999), p. 53-69 / Harvested from Czech Digital Mathematics Library
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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 $\omega ^{p'}$ belongs to the $A_1$ class of Muckenhoupt.

Publié le : 1999-01-01
Classification:  26A33,  42B25,  46E30,  47G10 
@article{119063,
     author = {Eleonor Ofelia Harboure and Oscar Salinas and Beatriz E. Viviani},
     title = {Relations between weighted Orlicz and $BMO\_\phi$ spaces through fractional integrals},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {40},
     year = {1999},
     pages = {53-69},
     zbl = {1060.46509},
     mrnumber = {1715202},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119063}
}

Harboure, Eleonor Ofelia; Salinas, Oscar; Viviani, Beatriz E. Relations between weighted Orlicz and $BMO_\phi$ spaces through fractional integrals. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 53-69. http://gdmltest.u-ga.fr/item/119063/

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