Estimates for L{\phi}-Lipschitz and L{\phi}-BMO Norms of Differential Forms

Abstract

In this paper, we define the L{\phi}-Lipschitz norm and L{\phi}-BMO norm of differential forms using Young functions, and prove the comparison theorems for the homotopy operator T on differential forms with L{\phi}-Lipschitz and L{\phi}-BMO norms. As applications, we give the L{\phi}-BMO norm estimate for conjugate A-harmonic tensors and the weighted L{\phi}-Lipschitz norm estimate for the homotopy operator T.