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Sharp norm estimates for composition operators and Hilbert‐type inequalities

Sharp norm estimates for composition operators and Hilbert‐type inequalities Let H2 denote the Hardy space of Dirichlet series f(s)=∑n⩾1ann−s with square summable coefficients and suppose that φ is a symbol generating a composition operator on H2 by Cφ(f)=f∘φ. Let ζ denote the Riemann zeta function and α0=1.48… the unique positive solution of the equation αζ(1+α)=2. We obtain sharp upper bounds for the norm of Cφ on H2 when 0<Reφ(+∞)−1/2⩽α0, by relating such sharp upper bounds to the best constant in a family of discrete Hilbert‐type inequalities. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Sharp norm estimates for composition operators and Hilbert‐type inequalities

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References (11)

Publisher
Wiley
Copyright
© 2017 London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms.12092
Publisher site
See Article on Publisher Site

Abstract

Let H2 denote the Hardy space of Dirichlet series f(s)=∑n⩾1ann−s with square summable coefficients and suppose that φ is a symbol generating a composition operator on H2 by Cφ(f)=f∘φ. Let ζ denote the Riemann zeta function and α0=1.48… the unique positive solution of the equation αζ(1+α)=2. We obtain sharp upper bounds for the norm of Cφ on H2 when 0<Reφ(+∞)−1/2⩽α0, by relating such sharp upper bounds to the best constant in a family of discrete Hilbert‐type inequalities.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Dec 1, 2017

Keywords: ; ;

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