Rocky Mountain Journal of Mathematics

Derivatives of Blaschke products in weighted mixed norm spaces

Atte Reijonen

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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
Received: 22 October 2017
First available in Project Euclid: 23 June 2019

Permanent link to this document
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

Keywords
Blaschke product doubling weight inner function mixed norm space separated sequence

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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