Coefficient estimates for $H^p$ spaces with $0<p<1$
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- by Ole Fredrik Brevig and Eero Saksman PDF
- Proc. Amer. Math. Soc. 148 (2020), 3911-3924 Request permission
Abstract:
Let $C(k,p)$ denote the smallest real number such that the estimate $|a_k|\leq C(k,p)\|f\|_{H^p}$ holds for every $f(z)=\sum _{n\geq 0}a_n z^n$ in the $H^p$ space of the unit disc. We compute $C(2,p)$ for $0<p<1$ and $C(3,2/3)$, and identify the functions attaining equality in the estimate.References
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Additional Information
- Ole Fredrik Brevig
- Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway
- MR Author ID: 1069722
- Email: ole.brevig@math.ntnu.no
- Eero Saksman
- Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway; and Department of Mathematics and Statistics, University of Helsinki, FI-00170 Helsinki, Finland
- MR Author ID: 315983
- Email: eero.saksman@helsinki.fi
- Received by editor(s): June 15, 2019
- Received by editor(s) in revised form: July 14, 2019, October 21, 2019, and January 13, 2020
- Published electronically: March 17, 2020
- Additional Notes: Some of the work in this paper was carried out during the workshop “Operator related Function Theory” at the Erwin Schrödinger Institute. The authors gratefully acknowledge the support of the ESI
- Communicated by: Stephan Ramon Garcia
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 3911-3924
- MSC (2010): Primary 30H10; Secondary 42A05
- DOI: https://doi.org/10.1090/proc/14995
- MathSciNet review: 4127835