Some higher norm inequalities for composition of power operators

[摘要] In this paper, we first prove the local $L^{s}$ norm estimate of composite operators $\triangle^{k}G^{m}(u)$ by use of the $L^{s}$ norm of u. Then we establish the local and global higher norm inequalities of $\triangle^{k}G^{m}(u)$. 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 $\triangle^{k}G^{m}(u)$.

[学科分类] 电力

[关键词] Power operators;Radon measure;Whitney cover;Higher norm inequalities