Weighted inequalities for potential operators on differential forms (Q962515)

The author extends a weak-type, two-weight inequality for potential operators [see \textit{D.\,Cruz-Uribe} and \textit{C.\,Pérez}, ``Two-weight, weak-type norm inequalities for fractional integrals, Calderón-Zygmund operators and commutators'', Indiana Univ.\ Math.\ J.\ 49, No.\,2, 697--721 (2000; Zbl 1033.42009)] to differential forms defined on an open set in \(\mathbb{R}^{n}\), and also proves a strong-type two-weight inequality for the solutions of the nonhomogeneous \(A\)-harmonic equation [for the scalar case, see \textit{E.\,Sawyer} and \textit{R.\,L.\thinspace Wheeden}, ``Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces'', Am.\ J.\ Math.\ 114, No.\,4, 813--874 (1992; Zbl 0783.42011)].