报告题目： An application of random operator theory: Bernstein-type inequalities 报 告 人： 方向 教授 报告人所在单位： 台湾中央大学 报告日期： 2019-09-27 星期五 报告时间： 10:00 -11:00 报告地点： 光华东主楼1403 报告摘要： An example of the Bernstein-type inequalities we will discuss is the following: For a polynomial $p(z)=c_0+c_1z+\cdots c_n z^n$ of degree $n$, the following reverse-Holder inequality holds for Hardy-norms, $$||p||_{H^{\frac{3}{2}}(\mathbb{D})} \ge \frac{C}{\sqrt[6]{n}} ||p||_{H^{{2}}(\mathbb{D})},$$ where the power $\frac{1}{6}$ is optimal. This is a deterministic result, and we derive it with probabilistic methods during our investigation of random operator theory on the Bergman space. 本年度学院报告总序号： 204