Norm of the generalized Hilbert operator on weighted Bergman spaces

RESUMO

Several upper bounds as well as one lower bound for the operator norm of the generalized Hilbert operator $\mathcal{H}_b$ acting on weighted Bergman spaces $A_{\alpha}^p$ are established. Moreover, under some mild assumptions, we obtain the exact norm of $\mathcal{H}_b$ on $ A_{\alpha}^p$.