Geodesic
The fractional integral between weighted Orlicz and $BMO_{\phi}$ spaces on spaces of homogeneous type
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 3, pp. 469-487.

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In this work we give sufficient and necessary conditions for the boundedness of the fractional integral operator acting between weighted Orlicz spaces and suitable $BMO_{\phi}$ spaces, in the general setting of spaces of homogeneous type. This result generalizes those contained in [P1] and [P2] about the boundedness of the same operator acting between weighted $L^{p}$ and Lipschitz integral spaces on $\Bbb R^n$. We also give some properties of the classes of pairs of weights appearing in connection with this boundedness.
Classification : 26A33, 42B25, 46E30, 46E35
Keywords: weights; Orlicz spaces; $BMO$; fractional integral 
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     title = {The fractional integral between weighted {Orlicz} and $BMO_{\phi}$ spaces on spaces of homogeneous type},
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Pradolini, Gladis; Salinas, Oscar. The fractional integral between weighted Orlicz and $BMO_{\phi}$ spaces on spaces of homogeneous type. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 3, pp. 469-487. http://geodesic.mathdoc.fr/item/CMUC_2003__44_3_a6/