Some strong (p, q)-type inequalities for the homotopy operator

Abstract We prove the boundedness of the homotopy operator in the weighted L p spaces. As extensions of ( p , p ) -type norm inequalities for the homotopy operator, we also establish some strong ( p , q ) -type norm inequalities with A r weights and power-type weights for the homotopy operator acting on differential forms. Finally, we obtain some estimates for singular integrals.