Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the exact value of the norm of the Hilbert matrix operator on
  weighted Bergman spaces   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 Karapetrovi\'{c}. We obtain a complete solution to
the conjecture for $\alpha \ge 0$ and
$2+\alpha+\sqrt{\alpha^2+\frac{7}{2}\alpha+3} \le p < 2(2+\alpha)$ and a
partial solution for $2+2\alpha < p <
2+\alpha+\sqrt{\alpha^2+\frac{7}{2}\alpha+3}.$ Moreover, we also show that the
conjecture is valid for small values of $\alpha$ when $2+2\alpha < p \le
3+2\alpha.$ Finally, the case $\alpha = 1$ is considered.

37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph