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 Aa is adressed. The norm was conjectured to be pi sin (2+alpha)pi p 2+alpha+alpha 2 + 72 alpha + 3 < p < 2(2+alpha) and a partial solution for 2+2 alpha < p < 2+alpha+alpha 2 + 27 alpha + 3. Moreover, we also show that the conjecture is valid for small values of alpha when 2 + 2 alpha < p < 3 + 2 alpha. Finally, the case alpha = 1 is considered. by Karapetrovic. We obtain a complete solution to the conjecture for alpha > 0 and