Some higher norm inequalities for composition of power operators

Journal of inequalities and applications

article

Huacan Li¹  Qunfang Li² 

[1] School of Science, JiangXi University of Science and Technology;Department of Mathematics, Ganzhou Teachers College

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

DOI  :  10.1186/s13660-020-02372-2

学科分类：电力

来源: SpringerOpen

【 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 $\triangle^{k}G^{m}(u)$.

【 授权许可】

CC BY