Illinois Journal of Mathematics

Bounds on the norm of the backward shift and related operators in Hardy and Bergman spaces

Timothy Ferguson

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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 $p=1$.

Article information

Illinois J. Math., Volume 61, Number 1-2 (2017), 81-96.

Received: 10 February 2017
Revised: 15 September 2017
First available in Project Euclid: 3 March 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B38: Operators on function spaces (general)
Secondary: 30H10: Hardy spaces 30H20: Bergman spaces, Fock spaces


Ferguson, Timothy. Bounds on the norm of the backward shift and related operators in Hardy and Bergman spaces. Illinois J. Math. 61 (2017), no. 1-2, 81--96. doi:10.1215/ijm/1520046210.

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