The fractional integral between Orlicz and BMO(phi) spaces on spaces of homogeneous type

Abstract

In this work we give sufficient and necessary conditions for the boundednessof the fractional integral operator acting between weighted Orlicz spaces and suitableBMOφ spaces, in the general setting of spaces of homogeneous type. This result generalizesthose contained in [P1] and [P2] about the boundedness of the same operator actingbetween weighted Lp and Lipschitz integral spaces on Rn. We also give some propertiesof the classes of pairs of weights appearing in connection with this boundednes.