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Endpoint Regularity of Multisublinear Fractional 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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In this paper we investigate the endpoint regularity properties of the multisublinear fractional maximal operators, which include the multisublinear Hardy–Littlewood maximal operator. We obtain some new bounds for the derivative of the one-dimensional multisublinear fractional maximal operators acting on the vector-valued function $\overrightarrow{f}=({{f}_{1}},...,{{f}_{m}})$ with all ${{f}_{j}}$ being $BV$-functions.

Keywords

42B2546E35multisublinear fractional maximal operatorsSobolev spacesbounded variation
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 3 , 01 September 2017 , pp. 586 - 603
Copyright
Copyright © Canadian Mathematical Society 2017

References

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