Open Access
Translator Disclaimer
Spring and Summer 2017 Bounds on the norm of the backward shift and related operators in Hardy and Bergman spaces
Timothy Ferguson
Illinois J. Math. 61(1-2): 81-96 (Spring and Summer 2017). DOI: 10.1215/ijm/1520046210

Abstract

We study bounds for the backward shift operator $f\mapsto(f(z)-f(0))/z$ and the related operator $f\mapsto f-f(0)$ on Hardy and Bergman spaces of analytic and harmonic functions. If $u$ is a real valued harmonic function, we also find a sharp bound on $M_{1}(r,u-u(0))$ in terms of $\|u\|_{h^{1}}$, where $M_{1}$ is the integral mean with $p=1$.

Citation

Download Citation

Timothy Ferguson. "Bounds on the norm of the backward shift and related operators in Hardy and Bergman spaces." Illinois J. Math. 61 (1-2) 81 - 96, Spring and Summer 2017. https://doi.org/10.1215/ijm/1520046210

Information

Received: 10 February 2017; Revised: 15 September 2017; Published: Spring and Summer 2017
First available in Project Euclid: 3 March 2018

zbMATH: 06864460
MathSciNet: MR3770837
Digital Object Identifier: 10.1215/ijm/1520046210

Subjects:
Primary: 47B38
Secondary: 30H10 , 30H20

Rights: Copyright © 2017 University of Illinois at Urbana-Champaign

JOURNAL ARTICLE
16 PAGES


SHARE
Vol.61 • No. 1-2 • Spring and Summer 2017
Back to Top