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NORM OF THE HILBERT MATRIX OPERATOR ON THE WEIGHTED BERGMAN SPACES
Published online by Cambridge University Press: 18 October 2017
Abstract
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*}
$\frac{\pi}{\sin{\frac{(\alpha+2)\pi}{p}}}$, while if 2 ≤ α +2 < p < 2(α+2), upper bound for the norm ∥H∥Ap,α → Ap,α, better then known, is obtained.
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- Research Article
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- Copyright © Glasgow Mathematical Journal Trust 2017
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