## Kodai Mathematical Journal

### Mean growth of the derivative of a Blaschke product

David Protas

#### Abstract

If $B$ is a Blaschke product with zeros $\{a_n\}$ and if $\sum_n(1-|a_n|)^{\alpha}$ is finite for some $\alpha \in (1/2,1]$, then limits are found on the rate of growth of $\int_0^{2\pi} |B'(re^{it}|^p\, dt$ in agreement with a known result for $\alpha \in (0,1/2)$. Also, a converse is established in the case of an interpolating Blaschke product, whenever $0<\alpha<1$.

#### Article information

Source
Kodai Math. J., Volume 27, Number 3 (2004), 354-359.

Dates
First available in Project Euclid: 28 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1104247356

Digital Object Identifier
doi:10.2996/kmj/1104247356

Mathematical Reviews number (MathSciNet)
MR2100928

Zentralblatt MATH identifier
1083.30033

#### Citation

Protas, David. Mean growth of the derivative of a Blaschke product. Kodai Math. J. 27 (2004), no. 3, 354--359. doi:10.2996/kmj/1104247356. https://projecteuclid.org/euclid.kmj/1104247356