Abstract: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.
Keywords: weights, Orlicz spaces, $BMO$, fractional integral
AMS Subject Classification: Primary 42B25