Lipschitz and BMO norm inequalities for the composite operator on differential forms

摘要

In this paper, we obtain Poincaré-type inequalities for the composite operator acting on differential forms and establish the L p $L^{p}$ , Lipschitz, and BMO norm estimates. We also give the weighted versions of the comparison theorems for the L p $L^{p}$ , Lipschitz, and BMO norms.