Norm of the generalized Hilbert operator on weighted Bergman spaces

Abstract: Several upper bounds as well as one lower bound for the operator norm of the generalized Hilbert operator $\mathcal{H}<em>b$ acting on weighted Bergman spaces $A</em>α<sup>p$ are established. Moreover, under some mild assumptions, we obtain the exact norm of $\mathcal{H}<em>b$ on $A</em>α<sup>p$.