Abstract
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.
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