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NORM OF THE HILBERT MATRIX OPERATOR ON THE WEIGHTED BERGMAN SPACES

Part of: Special classes of linear operators Spaces and algebras of analytic functions

Published online by Cambridge University Press:  18 October 2017

BOBAN KARAPETROVIĆ
BOBAN KARAPETROVIĆ*
Affiliation:
University of Belgrade, Faculty of Mathematics Studentski trg 16, Serbia e-mail: [email protected]
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Abstract

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We find the lower bound for the norm of the Hilbert matrix operator H on the weighted Bergman space Ap,α

\begin{equation*} \|H\|_{A^{p,\alpha}\rightarrow A^{p,\alpha}}\geq\frac{\pi}{\sin{\frac{(\alpha+2)\pi}{p}}}, \,\, \textnormal{for} \,\, 1<\alpha+2<p. \end{equation*}
We show that if 4 ≤ 2(α + 2) ≤ p, then ∥H∥Ap,α → Ap,α = $\frac{\pi}{\sin{\frac{(\alpha+2)\pi}{p}}}$, while if 2 ≤ α +2 < p < 2(α+2), upper bound for the norm ∥H∥Ap,α → Ap,α, better then known, is obtained.

MSC classification

Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
Secondary: 30H20: Bergman spaces, Fock spaces
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 3 , September 2018 , pp. 513 - 525
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

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