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

Abstract

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 L p ( v) to L q,∞ ( u), 1< p⩽ q<∞, provided the pair of weights ( u, v) verifies a Muckenhoupt condition with a “power-bump” on the weight u.