On the norm of the Hilbert matrix operator on weighted Bergman spaces.

It is known that the norm of the Hilbert matrix operator on weighted Bergman spaces A α p was conjectured by Karapetrović to be π sin ⁡ (α + 2) π p when α > − 1 and p > α + 2. The conjecture has been confirmed by Božin and Karapetrović in the case α = 0. In this paper we prove the conjecture for the cases both α = 1 and 0 < α ≤ 1 47. Moreover, we also show that the conjecture is valid when − 1 < α < 0 and p ≥ 2 (α + 2). [ABSTRACT FROM AUTHOR]