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In this paper, we first prove the local two-weight Caccioppoli inequalities for solutions to the nonhomogeneous A-harmonic equation of the form d*A(x, dω) = B(x, dω). Then, as applications of the local results, we prove the global two-weight Caccioppoli-type inequalities for these solutions on Riemannian manifolds.

Two-weight Caccioppoli inequalities for solutions of nonhomogeneous 𝐴-harmonic equations on Riemannian manifolds