Weighted Integral Means of Mixed Areas and Lengths under Holomorphic Mappings

Jie Xiao, Wen Xu

This note addresses monotonic growths and logarithmic convexities of the weighted ($(1-t^2{)}^{\alpha }d{t}^2$, $-\infty <\alpha <\infty$, $0<t<1$) integral means ${\mathsf{A}}_{\alpha ,\beta }(f,\cdot )$ and $\ma…