## Rocky Mountain Journal of Mathematics

### Derivatives of Blaschke products in weighted mixed norm spaces

Atte Reijonen

#### Abstract

For $1/2\lt p\lt \infty$, $0\lt q\lt \infty$ and a certain two-sided doubling weight $\omega$, we give a condition for the zeros of a Blaschke product $B$ which guarantees that $$\|B'\|_{A^{p,q}_\omega }^q=\int _0^1 \bigg (\int _0^{2\pi } |B'(re^{i\theta })|^p d\theta \bigg )^{q/p} \omega (r)\,dr\lt \infty .$$ In addition, it is shown that the condition is necessary if the zero-sequence is a finite union of separated sequences.

#### Note

This research was supported in part by Academy of Finland project Nos. 268009 and 286877, The Finnish Cultural Foundation and a JSPS Postdoctoral Fellowship for North American and European Researchers.

#### Article information

Source
Rocky Mountain J. Math., Volume 49, Number 2 (2019), 627-643.

Dates
First available in Project Euclid: 23 June 2019

https://projecteuclid.org/euclid.rmjm/1561318397

Digital Object Identifier
doi:10.1216/RMJ-2019-49-2-627

Mathematical Reviews number (MathSciNet)
MR3973244

Zentralblatt MATH identifier
07079988

Subjects
Primary: 30J10: Blaschke products
Secondary: 30J05: Inner functions

#### Citation

Reijonen, Atte. Derivatives of Blaschke products in weighted mixed norm spaces. Rocky Mountain J. Math. 49 (2019), no. 2, 627--643. doi:10.1216/RMJ-2019-49-2-627. https://projecteuclid.org/euclid.rmjm/1561318397

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