Weighted inequalities for potential operators on differential forms. (English) Zbl 1193.47054

The author extends a weak-type, two-weight inequality for potential operators [see D.Cruz-Uribe and 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 E.Sawyer and R.L.Wheeden, “Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces”, Am.J.Math.114, No.4, 813–874 (1992; Zbl 0783.42011)].


47G40 Potential operators
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
58A10 Differential forms in global analysis
26D10 Inequalities involving derivatives and differential and integral operators
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