Geodesic
NORM OF THE HILBERT MATRIX OPERATOR ON THE WEIGHTED BERGMAN SPACES
Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 513-525

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DOI

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. 
KARAPETROVIĆ, BOBAN. NORM OF THE HILBERT MATRIX OPERATOR ON THE WEIGHTED BERGMAN SPACES. Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 513-525. doi: 10.1017/S0017089517000258
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     author = {KARAPETROVI\'C, BOBAN},
     title = {NORM {OF} {THE} {HILBERT} {MATRIX} {OPERATOR} {ON} {THE} {WEIGHTED} {BERGMAN} {SPACES}},
     journal = {Glasgow mathematical journal},
     pages = {513--525},
     year = {2018},
     volume = {60},
     number = {3},
     doi = {10.1017/S0017089517000258},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089517000258/}
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