Some higher norm inequalities for composition of power operators

Abstract

In this paper, we first prove the local L s norm estimate of composite operators k G m (u) by use of the L s norm of u. Then we establish the local and global higher norm inequalities of k G m (u). Simultaneously, we also give a global higher norm estimate with Radon measure. Finally, as applications of these results, we give two examples to estimate the higher norm of k G m (u).