标题： 二阶离散 Hardy-Littlewood 极大函数导数 显示英文标题

标题： The second derivative of the discrete Hardy-Littlewood maximal function

摘要： Hardy-Littlewood极大函数的正则性，在离散和连续背景下，以及在中心和非中心变体中，过去二十年来受到了深入研究。 但迄今为止的努力主要集中在一阶可微性和变分上，因为已知在连续背景下高阶正则性是不可能的。 这篇简短的注记给出了离散非中心极大函数高阶正则性的第一个积极结果。 显示英文摘要

摘要： The regularity of the Hardy-Littlewood maximal function, in both discrete and continuous contexts, and for both centered and noncentered variants, has been subjected to intense study for the last two decades. But efforts so far have concentrated on first order differentiability and variation, as it is known that in the continuous context higher order regularity is impossible. This short note gives the first positive result on the higher order regularity of the discrete noncentered maximal function.