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 .