标题： 对递减函数的对偶Hardy算子减去单位算子的最佳界 显示英文标题

标题： Best bounds for the dual Hardy operator minus identity on decreasing functions

摘要： 从单位算子$I$到$H^*$，即 Hardy 平均算子的对偶，在 Lebesgue 空间中非负非增函数的锥上的距离被研究。得到了精确值。还给出了这两个算子在相同锥上作用时的差值$H^*-I$的最优下界。对 A. Ben Said、S. Boza 和 J. Soria 在《The norm of Hardy-type oscillation operators in the discrete and continuous settings》中提出的猜想给出了肯定回答。预印本，2024年。此外，还给出了在锥上作用的算子$H-I$和$H^*-I$之间的直接比较，具有最优常数。 显示英文摘要

摘要： The distance from the identity operator $I$ to $H^*$, the dual of the Hardy averaging operator, is studied on the cone of nonnegative, nonincreasing functions in Lebesgue space. The exact value is obtained. Optimal lower bounds are also given for difference, $H^*-I$, of these two operators acting on the same cone. A positive answer is given to a conjecture made in ``The norm of Hardy-type oscillation operators in the discrete and continuous settings'' by A. Ben Said, S. Boza, and J. Soria. Preprint, 2024. In addition, a direct comparison, with optimal constants, is given between the operators $H-I$ and $H^*-I$ acting on the cone.