Boundedness characterization of composite operator with Orlicz–Lipschitz norm and Orlicz-BMO norm

Abstract

In this paper, we establish the boundedness estimates for the composition of the homotopy operator $T$ and the potential operator $T_{\Phi }$ on differential forms with Orlicz–Lipschitz norm and Orlicz-BMO norm which are defined by a Young function. Moreover, we derive the two-weight norm inequalities for the composite operator $T\circ T_{\Phi }$ using the Poincaré-type inequality with $A_r^{\lambda }(\Omega )$-weight. Finally, we demonstrate some applications of our main results.