On the boundedness of the total variation of the logarithm of a Blaschke product

  • Ya. V. Kondratyuk


We establish that, for a Blaschke product B(z) convergent in the unit disk, the condition - ∞ < \(\smallint _0^1 \log (1 - t)n(t,B)dt\) is sufficient for the total variation of logB to be bounded on a circle of radiusr, 0 <r < 1. For products B(z) with zeros concentrated on a single ray, this condition is also necessary. Here, n(t, B) denotes the number of zeros of the functionB (z) in a disk of radiust.
How to Cite
KondratyukY. V. “On the Boundedness of the Total Variation of the Logarithm of a Blaschke Product”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 51, no. 11, Nov. 1999, pp. 1449–1455, https://umj.imath.kiev.ua/index.php/umj/article/view/4746.
Research articles