On the derivative of infinite Blaschke products (Q1425772)

For any given positive and continuous function \(\phi\) defined on \([0,1)\) with \(\phi(r)\to\infty\) as \(r\to 1\), the authors constructed two new and quite different classes of examples of infinite Blaschke products \(B\) in \(| z| <1\) such that every point of \(| z| =1\) is an accumulation point of the sequence of zeros of \(B\) and \[ \frac{1}{2\pi}\int_{-\pi}^{\pi}| B'(re^{it})| \,dt=O(\phi(r)) \] as \(r\to 1\).