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

Bi, Hui

J. Inequal. Appl. 2010, Article ID 713625, 13 p. (2010).

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)].

Reviewer: Mihai Pascu (Bucureşti)

MSC:

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

Keywords:

potential operators; two-weight conditions; differential forms; \(A\)-harmonic equation

Citations:

Zbl 1033.42009; Zbl 0783.42011

References:

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[5]	Cruz-Uribe D, Pérez C: Two-weight, weak-type norm inequalities for fractional integrals, Calderón-Zygmund operators and commutators. Indiana University Mathematics Journal 2000, 49(2):697-721. · Zbl 1033.42009
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