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

\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 ∥HApAp = $\frac{\pi}{\sin{\frac{(\alpha+2)\pi}{p}}}$ , while if 2 ≤ α +2 < p < 2(α+2), upper bound for the norm ∥HApAp, better then known, is obtained.



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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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