In the paper, we investigate the iterated non-centered Hardy-Littlewood maximal function and the iterated centered Hardy-Littlewood maximal function. We prove that the limit of the iterated maximal function is just a fixed point of maximal operator. As an application of the fixed point theory, we finally obtain that the fixed point is||f||∞ for non-centered Hardy-Littlewood maximal operator. The same is true for the centered Hardy-Littlewood maximal operator only for n=1,2.
WANG Zequn
,
YAN Dunyan
. Iterated Hardy-Littlewood maximal function[J]. Journal of University of Chinese Academy of Sciences, 2018
, 35(4)
: 433
-437
.
DOI: 10.7523/j.issn.2095-6134.2018.04.001
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