Monomial basis in Korenblum type spaces of analytic functions
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- by José Bonet, Wolfgang Lusky and Jari Taskinen PDF
- Proc. Amer. Math. Soc. 146 (2018), 5269-5278 Request permission
Abstract:
It is shown that the monomials $\Lambda =(z^n)_{n=0}^{\infty }$ are a Schauder basis of the Fréchet spaces $A_+^{-\gamma }, \ \gamma \geq 0,$ that consists of all the analytic functions $f$ on the unit disc such that $(1-|z|)^{\mu }|f(z)|$ is bounded for all $\mu > \gamma$. Lusky proved that $\Lambda$ is not a Schauder basis for the closure of the polynomials in weighted Banach spaces of analytic functions of type $H^{\infty }$. A sequence space representation of the Fréchet space $A_+^{-\gamma }$ is presented. The case of (LB)-spaces $A_{-}^{-\gamma }, \ \gamma > 0,$ that are defined as unions of weighted Banach spaces is also studied.References
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Additional Information
- José Bonet
- Affiliation: Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, E-46071 Valencia, Spain
- ORCID: 0000-0002-9096-6380
- Email: jbonet@mat.upv.es
- Wolfgang Lusky
- Affiliation: Institut für Mathematik, Universität Paderborn, D-33098 Paderborn, Germany
- MR Author ID: 199549
- Email: lusky@uni-paderborn.de
- Jari Taskinen
- Affiliation: Department of Mathematics and Statistics, P.O. Box 68, University of Helsinki, 00014 Helsinki, Finland
- MR Author ID: 170995
- Email: jari.taskinen@helsinki.fi
- Received by editor(s): January 17, 2018
- Received by editor(s) in revised form: April 16, 2018
- Published electronically: September 17, 2018
- Additional Notes: Research of the first author was partially supported by the project MTM2016-76647-P.
Research of the third author was partially supported by the Väisälä Foundation of the Finnish Academy of Sciences and Letters. - Communicated by: Thomas Schlumprecht
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 5269-5278
- MSC (2010): Primary 46E10; Secondary 46A35, 46A45, 46E15
- DOI: https://doi.org/10.1090/proc/14195
- MathSciNet review: 3866866