Weighted Integral Means of Mixed Areas and Lengths under Holomorphic Mappings
Weighted Integral Means of Mixed Areas and Lengths under Holomorphic Mappings
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DOI：
10.4208/ata.2014.v30.n1.1
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发表时间：
2011-05
期刊：
影响因子：
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通讯作者：
J. Xiao;Wen Xu
中科院分区：
文献类型：
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作者：
J. Xiao;Wen Xu
本文讨论加权($(1-t^2)^\αdt^2$，$-\inty；\inty$，$0<；t<；1$)积分是指混合区域$(pi r^2)^{-\β}A(f，r)$和混合长度$(2\pi r)^{-\β}L(f，r)$($0\le\beta)$和$\mathsf{L}_{\α，\beta}(f，\cdot)$和$\mathsf{A}_{\α，\β}(f，\cdot)$和$\mathsf{A}_{\α，\beta}(f，\cdot)$和$\mathsf{A}_{\α，\β}(f，\cdot)$和$(pi r^2)^{-\β}A(f，r)$和$0<；从单位圆盘$\mathbb D$到有限复平面$\mathbb C$的全纯映射$f$下的$f(r\mathbb D)$和$\Partial f(r\mathbb D)$的1$)。
This note addresses monotonic growths and logarithmic convexities of the weighted ($(1-t^2)^\alpha dt^2$, $-\infty<\alpha<\infty$, $0<t<1$) integral means $\mathsf{A}_{\alpha,\beta}(f,\cdot)$ and $\mathsf{L}_{\alpha,\beta}(f,\cdot)$ of the mixed area $(\pi r^2)^{-\beta}A(f,r)$ and the mixed length $(2\pi r)^{-\beta}L(f,r)$ ($0\le\beta\le 1$ and $0<r<1$) of $f(r\mathbb D)$ and $\partial f(r\mathbb D)$ under a holomorphic map $f$ from the unit disk $\mathbb D$ into the finite complex plane $\mathbb C$.