We prove that there is an absolute constant A > 0 such that $$\begin{array}{l} \begin{array}{*{20}{c}} {\max } \\ { - 1 \le x \le 1} \\ \end{array}|P'(x)| \ge A\sqrt {n \cdot } \begin{array}{*{20}{c}} {\max } \\ { - 1 \le x \le 1} \\ \end{array}\,|P(x)| \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \\ \end{array}$$ for an arbitrary algebraic polynomial P of degree n whose zeros lie in the half-disk $$\left\{ {z:|z| \le 1,{\mathop{\rm Im}\nolimits} z \ge 0} \right\}$$.

中文翻译：

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零点位于上单元半圆盘的多项式的单位区间上的逆马尔可夫不等式

我们证明存在一个绝对常数 A > 0 使得 $$\begin{array}{l} \begin{array}{*{20}{c}} {\max } \\ { - 1 \le x \ le 1} \\ \end{数组}|P'(x)| \ge A\sqrt {n \cdot } \begin{array}{*{20}{c}} {\max} \\ { - 1 \le x \le 1} \\ \end{array}\,| P(x)| \\ \、\、\、\、\、\、\、\、\、\、\、\、\、\、\、\、\、\、\、\、\、\、\、\、 \,\,\,\,\,\,\,\,\,\,\,\,\, \\ \end{array}$$ 用于零点位于一半的 n 阶任意代数多项式 P -磁盘 $$\left\{ {z:|z| \le 1,{\mathop{\rm Im}\nolimits} z \ge 0} \right\}$$。