Norm Comparison Estimates for the Composite Operator

Abstract

This paper obtains the Lipschitz and BMO norm estimates for the composite operator 𝕄s∘P applied to differential forms. Here, 𝕄s is the Hardy-Littlewood maximal operator, and P is the potential operator. As applications, we obtain the norm estimates for the Jacobian subdeterminant and the generalized solution of the quasilinear elliptic equation.