2026/07/26 by Bingyang Hu, Jie Xiao, Xiaojing Zhou
#math.CV
We prove that there exist two Bloch functions f1 and f2 on \mathbb D such that |f1(z)|+|f2(z)| ≥ (log(1)/(1-|z|))1/2, z∈\mathbb D, thereby resolving an open problem posed in 2008 by Girela, Peláez, Pérez-González and Rättyä. Our proof is based on a new Szegő-type recursion involving \mathbb C2-valued polynomials and their reciprocal polynomials.