We nd necessary conditions and su cient conditions on weights u(:) a n d v(:) for which the fractional integral operator I is bounded from the weighted Lebesgue spaces L p v into L q u whenever 1 < q < p < 1 and 0 < < n .Actually such a boundedness is characterized for a large class of weights.
Yves Rakotondratsimba (Thu,) studied this question.