On the Regularity of the Multisublinear Maximal Functions

Canadian mathematical bulletin

Feng Liu²  Huoxiong Wu¹ 

[1] School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, P. R. China;College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, P. R. China

关键词: regularity;    multisublinear maximal operator;    Sobolev spaces;    partial deviative;    quasicontinuity;   

DOI  :  10.4153/CMB-2014-070-7

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

This paper is concerned with the study ofthe regularity for the multisublinear maximal operator. It isproved that the multisublinear maximal operator is bounded onfirst-order Sobolev spaces. Moreover, two key point-wiseinequalities for the partial derivatives of the multisublinearmaximal functions are established. As an application, thequasi-continuity on the multisublinear maximal function is alsoobtained.

【 授权许可】

Unknown