Weighted inequalities for integral operators on Lebesgue and BMOγ(ω) spaces

Abstract

We characterize the power weights ω for which the fractional type operator Tα , β is bounded from Lp(ωp) into Lq(ωq) for 1 < p< n/ (n- (α+ β)) and 1 / q= 1 / p- (n- (α+ β)) / n. If n/ (n- (α+ β)) ≤ p< n/ (n- (α+ β) - 1) + we prove that Tα , β is bounded from a weighted weak Lp space into a suitable weighted BMOδ space for weights satisfying a doubling condition and a reverse Hölder condition. Also, we prove the boundedness of Tα , β from a weighted local space BMO0γ into a weighted BMOδ space, for weights satisfying a doubling condition.