Logarithmic Convexity of Area Integral Means for Analytic Functions
Keyword(s):
We show that the $L^2$ integral mean on $r\mathsf{D}$ of an analytic function in the unit disk $\mathsf{D}$ with respect to the weighted area measure $(1-|z|^2)^\alpha\,dA(z)$, where $-3\le\alpha\le0$, is a logarithmically convex function of $r$ on $(0,1)$. We also show that the range $[-3,0]$ for $\alpha$ is best possible.
2014 ◽
Vol 98
(1)
◽
pp. 117-128
◽
Keyword(s):
2018 ◽
Vol 61
(3)
◽
pp. 509-517
◽
Keyword(s):
2006 ◽
Vol 2006
◽
pp. 1-6
◽
Keyword(s):
2015 ◽
Vol 99
(3)
◽
pp. 315-333
Keyword(s):
Keyword(s):
2016 ◽
Vol 24
(1)
◽
pp. 353-369
Keyword(s):