Translator Disclaimer
2019 Derivatives of Blaschke products in weighted mixed norm spaces
Atte Reijonen
Rocky Mountain J. Math. 49(2): 627-643 (2019). DOI: 10.1216/RMJ-2019-49-2-627

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.

Funding Statement

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.

Citation

Download Citation

Atte Reijonen. "Derivatives of Blaschke products in weighted mixed norm spaces." Rocky Mountain J. Math. 49 (2) 627 - 643, 2019. https://doi.org/10.1216/RMJ-2019-49-2-627

Information

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

zbMATH: 07079988
MathSciNet: MR3973244
Digital Object Identifier: 10.1216/RMJ-2019-49-2-627

Subjects:
Primary: 30J10
Secondary: 30J05

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

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
17 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.49 • No. 2 • 2019
Back to Top