@Article{ATA-30-1,
author = {J. Xiao and W. Xu},
title = {Weighted Integral Means of Mixed Areas and Lengths Under Holomorphic Mappings},
journal = {Analysis in Theory and Applications},
year = {2014},
volume = {30},
number = {1},
pages = {1--19},
abstract = {<p style="text-align: justify;">This note addresses monotonic growths and logarithmic convexities of the weighted ($(1-t^2)^\alpha dt^2$, $-\infty &lt;\alpha &lt;\infty$, $0&lt; t&lt; 1$) 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 $0&lt; r&lt; 1$) 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 $\mathbb C$.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2014.v30.n1.1},
url = {http://global-sci.org/intro/article_detail/ata/4470.html}
}