论文标题
关于Hilbert Matrix操作员在加权伯格曼空间的确切价值
On the exact value of the norm of the Hilbert matrix operator on weighted Bergman spaces
论文作者
论文摘要
在本文中，在加权伯格曼空间$ a^p_α$上找到希尔伯特矩阵操作员的确切价值的开放问题是受欢迎的。标准被Karapetrović猜想为$ \fracπ{\ sin \ frac {（2+α）π} {p}}} $。我们为$α\ ge 0 $和$ 2+α+\ sqrt {α^2+\ frac {7} {2} {2}α+3} \ le p <2（2+α）$和$ 2+2α<p <p <p <p <p <p <p <2} 2+α+\ sqrt {α^2+\ frac {7} {2} {2}α+3}。$。此外，我们还表明，当$ 2+2α<p \ p \ le 3+2α时，猜测对于$α$的小值有效
In this article, the open problem of finding the exact value of the norm of the Hilbert matrix operator on weighted Bergman spaces $A^p_α$ is adressed. The norm was conjectured to be $\fracπ{\sin \frac{(2+α)π}{p}}$ by Karapetrović. We obtain a complete solution to the conjecture for $α\ge 0$ and $2+α+\sqrt{α^2+\frac{7}{2}α+3} \le p < 2(2+α)$ and a partial solution for $2+2α< p < 2+α+\sqrt{α^2+\frac{7}{2}α+3}.$ Moreover, we also show that the conjecture is valid for small values of $α$ when $2+2α< p \le 3+2α.$ Finally, the case $α= 1$ is considered.
