Logarithmic Convexity of Area Integral Means for Analytic Functions - Wang, Chunjie; Zhu, Kehe (MATHEMATICA SCANDINAVICA, 2014)
We show that the L^2 integral mean on rD of an analytic function in the unit disk D with respect to the weighted area measure (1-|z|^2)^α dA(z), where -3α0, is a logarithmically convex function of r on (0,1). We also show that the range [-3,0] for α is best possible.