Translator Disclaimer
December 2018 Operators on Fock-type and weighted spaces of entire functions
Oscar Blasco
Funct. Approx. Comment. Math. 59(2): 175-189 (December 2018). DOI: 10.7169/facm/1708

Abstract

Let us denote by $\mathcal F_1^\phi(\mathbb C)$ the space of entire functions $f\in \mathcal H(\C)$ such that $\int_\mathbb C |f(z)|e^{-\phi(|z|)}dm(z)<\infty$, where $\phi:(0,\infty)\to \mathbb R^+$ is assumed to be continuous and non-decreasing. Also given a continuous non-increasing function $v:(0,\infty)\to \mathbb R^+$ and a complex Banach space $X$, we write $H^\infty_v(\mathbb C,X)$ for the space of $X$-valued entire functions $F$ such that $\sup_{z\in \C} v(z)\|F(z)\|<\infty$. We find a very general class of weights $\phi$ and $v$ for which the space of bounded operators $\mathcal L(\mathcal F_1^\phi(\mathbb C),X)$ can be identified with $H^\infty_v(\mathbb C, X)$.

Citation

Download Citation

Oscar Blasco. "Operators on Fock-type and weighted spaces of entire functions." Funct. Approx. Comment. Math. 59 (2) 175 - 189, December 2018. https://doi.org/10.7169/facm/1708

Information

Published: December 2018
First available in Project Euclid: 26 October 2018

zbMATH: 07055551
MathSciNet: MR3892394
Digital Object Identifier: 10.7169/facm/1708

Subjects:
Primary: 30H20
Secondary: 46E40

Keywords: entire function , Fock-type spaces , weighted spaces

Rights: Copyright © 2018 Adam Mickiewicz University

JOURNAL ARTICLE
15 PAGES

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

SHARE
Vol.59 • No. 2 • December 2018
Back to Top