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On the Regularity of the Multisublinear Maximal Functions

Published online by Cambridge University Press:  20 November 2018

Feng Liu  and
Huoxiong Wu
Feng Liu
Affiliation:
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, P. R. China e-mail: liufeng860314@163.com
Huoxiong Wu
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, P. R. China e-mail: huoxwu@xmu.edu.cn
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Abstract

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This paper is concerned with the study of the regularity for the multisublinear maximal operator. It is proved that the multisublinear maximal operator is bounded on first-order Sobolev spaces. Moreover, two key point-wise inequalities for the partial derivatives of the multisublinear maximal functions are established. As an application, the quasi-continuity on the multisublinear maximal function is also obtained.

Keywords

42B2546E35regularitymultisublinear maximal operatorSobolev spacespartial derivativequasicontinuity
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 4 , 01 December 2015 , pp. 808 - 817
Copyright
Copyright © Canadian Mathematical Society 2015

References

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