研究迭代的非中心型哈代-李特伍德极大函数和迭代的中心型哈代-李特伍德极大函数。证明迭代极大函数的极限是极大算子的一个不动点。作为不动点理论的一个应用，最终得到，对于非中心型哈代-李特伍德极大算子，这个不动点处处为||f||∞。对于中心型哈代-李特伍德极大算子，仅在n=1，2时有相同的结果。
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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