Generalized Hilbert matrix operators acting on Bergman spaces

In this article we study the generalized Hilbert matrix operator ${\mathrm{\Gamma }}_{\mu }$ acting on the Bergman spaces $A^p$ of the unit disc for $1\le p<\mathrm{\infty }$. In particular, we characterize the measures $\mu$ for which the operator ${\mathrm{\Gamma }}_{\mu }$ is bounded and we provide estimates of its operator norm. Finally, we also describe when ${\mathrm{\Gamma }}_{\mu }$ is compact by computing its essential norm.