Liu Tian

The norm of the Hilbert matrix operator on Bergman spaces

Karapetrovi\'c conjectured that the norm of the Hilbert matrix operator on the Bergman space $A^p_\alpha$ is equal to $\pi/\sin((2+\alpha)\pi/p)$ when $-1<\alpha \frac{1}{47}$ and $\alpha \not=1$.