## Illinois Journal of Mathematics

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

Timothy Ferguson

#### 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 $p=1$.

#### Article information

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

Dates
Revised: 15 September 2017
First available in Project Euclid: 3 March 2018

https://projecteuclid.org/euclid.ijm/1520046210

Digital Object Identifier
doi:10.1215/ijm/1520046210

Mathematical Reviews number (MathSciNet)
MR3770837

Zentralblatt MATH identifier
06864460

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

#### Citation

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. https://projecteuclid.org/euclid.ijm/1520046210

#### References

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