Norm estimates of weighted composition operators pertaining to the Hilbert matrix

Abstract

Copyright © 2018, arXiv, All rights reserved. Very recently, Božin and Karapetrović [4] solved a conjecture by proving that the norm of the Hilbert matrix operator H on the Bergman space Apis equal to π/sin( 2π/p ) for 2 < p < 4. In this article we present a partly new and simplified proof of this result. Moreover, we calculate the exact value of the norm of H defined on the Korenblum spaces H∞αfor 0 < α < 1.Primary 47B38, Secondary 30H20