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A NOTE ON THE ENDPOINT REGULARITY OF THE HARDY–LITTLEWOOD MAXIMAL FUNCTIONS

Published online by Cambridge University Press:  11 December 2015

FENG LIU*
Affiliation:
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, PR China email liufeng860314@163.com
TING CHEN
Affiliation:
School of Mathematics, University of Edinburgh, EH9 3JZ, UK email t.chen-16@sms.ed.ac.uk
HUOXIONG WU
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, PR China email huoxwu@xmu.edu.cn
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Abstract

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In this note we give a simple proof of the endpoint regularity for the uncentred Hardy–Littlewood maximal function on $\mathbb{R}$. Our proof is based on identities for the local maximum points of the corresponding maximal functions, which are of interest in their own right.

Type
Research Article
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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