Illinois Journal of Mathematics

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

Timothy Ferguson

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Permanent link to this document
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


Export citation

References

  • H. Bohr, A theorem concerning power series, Proc. Lond. Math. Soc. (2) 13 (1914), 1–5.
  • P. Duren, Theory of $H\sp{p}$ spaces, Pure and Applied Mathematics, vol. 38, Academic Press, New York, 1970.
  • P. Duren and A. Schuster, Bergman spaces, Mathematical Surveys and Monographs, vol. 100, American Mathematical Society, Providence, RI, 2004.
  • J. B. Garnett and D. E. Marshall, Harmonic measure, New Mathematical Monographs, vol. 2, Cambridge University Press, Cambridge, 2005.