Sharp norm estimates for composition operators and Hilbert-type inequalities
Journal article, Peer reviewed
Accepted version
Permanent lenke
http://hdl.handle.net/11250/2492763Utgivelsesdato
2017Metadata
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- Institutt for matematiske fag [2531]
- Publikasjoner fra CRIStin - NTNU [38525]
Originalversjon
Bulletin of the London Mathematical Society. 2017, 49 (6), 965-978. 10.1112/blms.12092Sammendrag
Let H 2 denote the Hardy space of Dirichlet series f ( s ) = ∑ n ⩾ 1 a n n − s with square summable coefficients and suppose that φ is a symbol generating a composition operator on H 2 by C φ ( f ) = f ∘ φ . Let ζ denote the Riemann zeta function and α 0 = 1.48 … the unique positive solution of the equation α ζ ( 1 + α ) = 2 . We obtain sharp upper bounds for the norm of C φ on H 2 when 0 < Re φ ( + ∞ ) − 1 / 2 ⩽ α 0 , by relating such sharp upper bounds to the best constant in a family of discrete Hilbert‐type inequalities.