Zygmund's type inequality to the polar derivative of a polynomial

On an inequality concerning the polar derivative of a polynomial

In this paper, we present a correct proof of an $L_p$-inequality concerning the polar derivative of a polynomial with restricted zeros. We also extend Zygmund's inequality to the polar derivative of a polynomial.

希洛夫边界上的Fefferman–Stein型不等式及其应用

On Fefferman--Stein type inequality on Shilov boundaries and applications

本文在希洛夫边界上建立面积积分与非切向极大函数的Fefferman–Stein型不等式，规避傅里叶变换与群结构的使用，得到乘积Hardy空间刻画及乘积Calderón–Zygmund算子的弱型端点估计。

Charatheodory and Smirnov type theorem for harmonic mappings

We prove a version of Smirnov type theorem and Charatheodory type theorem for a harmonic homeomorphism of the unit disk onto a Jordan surface with rectifiable boundary. Further we establish the classical isoperimetric inequality and Riesz--Zygmund inequality for Jordan harmonic surfaces without any smoothness assumptions of the boundary.

On an inequality concerning the polar derivative of a polynomial with restricted zeros

Let $D_αP(z)=nP(z)+(α-z)P^{\prime}(z)$ denote the polar derivative of a polynomial $P(z)$ of degree $n$ with respect to a point $α\in\mathbb{C}.$ In this paper, we present a correct proof, independent of Laguerre's theorem, of an inequality concerning the polar derivative of a polynomial with restricted zeros recently formulated by K. K. Dewan, Naresh Singh, Abdullah Mir, [Extensions of some polynomial inequalities to the polar derivative, \emph{J. Math. Anal. Appl.,} \textbf{352} (2009) 807-815].

关于 $L^p$-极体的 Santaló 不等式

A Santaló inequality for the $L^p$-polar body

本文将对称凸体的 $L^p$-Santaló 不等式推广至任意凸体，借助 $L^p$-Santaló 点平移与逐次 Steiner 对称化完成证明，并导出管域 Bergman 核的最优上界。

Bergman投影算子的端点估计及Bloch空间和$H^\infty$的新刻画

Endpoint Estimates for Bergman Commutators and New Characterizations of the Bloch Space and $H^\infty$

本文通过Bergman投影算子与共轭Bloch符号函数的交换子研究，给出了Bloch空间和$H^\infty$的新刻画及$\LlogL$型分布不等式的端点估计。