TY - JOUR AU - Lindström, Mikael AU - Miihkinen, Santeri AU - Wikman, Niklas PY - 2021/06/24 Y2 - 2024/03/29 TI - On the exact value of the norm of the Hilbert matrix operator on weighted Bergman spaces JF - Annales Fennici Mathematici JA - Ann. Fenn. Math. VL - 46 IS - 1 SE - Articles DO - UR - https://afm.journal.fi/article/view/109770 SP - 201-224 AB - <pre>In this article, the open problem of finding the exact value of the norm of the Hilbert matrix operator on weighted Bergman spaces \(A^p_\alpha\) is adressed. The norm was conjectured to be \(\frac{\pi}{\sin \frac{(2+\alpha)\pi}{p}}\) by Karapetrovic. We obtain a complete solution to the conjecture for \(\alpha &gt; 0\) and \(2+\alpha+\sqrt{\alpha^2+\frac{7}{2}\alpha+3} \le p &lt; 2(2+\alpha)\) and a partial solution for \(2+2\alpha &lt; p &lt; 2+\alpha+\sqrt{\alpha^2+\frac{7}{2}\alpha+3}\). Moreover, we also show that the conjecture is valid for small values of \(\alpha\) when \(2+2\alpha &lt; p \le 3+2\alpha\). Finally, the case \(\alpha = 1\) is considered.</pre> ER -