Fractional integrals, potential operators and two-weight, weak type norm inequalities on spaces of homogeneous type

We prove two-weight, weak type norm inequalities for potential operators and fractional integrals defined on spaces of homogeneous type. We show that the operators in question are bounded from Lp(v) to Lq,∞(u), 1 < p q < ∞, provided the pair of weights (u, v) verifies a Muckenhoupt condition with a “power-bump” on the weight u.  2004 Elsevier Inc. All rights reserved.