Abstract
We develop the weak-type and strong-type inequalities for potential operators under two-weight conditions to the versions of differential forms. We also obtain some estimates for potential operators applied to the solutions of the nonhomogeneous A-harmonic equation.
Highlights
Weighted Inequalities for Potential Operators on Differential FormsWe obtain some estimates for potential operators applied to the solutions of the nonhomogeneous A-harmonic equation
In recent years, differential forms as the extensions of functions have been rapidly developed.Many important results have been obtained and been widely used in PDEs, potential theory, nonlinear elasticity theory, and so forth; see 1–3
From 1, if ω is a differential form defined in a bounded, convex domain M, there is a decomposition ω d Tω T dω, 1.2 where T is called a homotopy operator
Summary
We obtain some estimates for potential operators applied to the solutions of the nonhomogeneous A-harmonic equation
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