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

Abstract

It is known that the norm of the Hilbert matrix operator on weighted Bergman spaces Aαp was conjectured by Karapetrović to be πsin⁡(α+2)πp 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≤147. Moreover, we also show that the conjecture is valid when −1<α<0 and p≥2(α+2).