The Higher Integrability of Commutators of Calderón-Zygmund Singular Integral Operators on Differential Forms

Abstract

In this article, the higher integrability of commutators of Calderón-Zygmund singular integral operators on differential forms is derived. Also, the higher order Poincaré-type inequalities for the commutators acting on the solutions of Dirac-harmonic equations are obtained. Finally, some applications of the main results are demonstrated by examples.