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In this article, we study the generalized Hilbert matrix operator Γ μ acting on the Bergman spaces A p of the unit disc for 1 ≤ p < ∞ . In particular, we characterize the measures μ for which the operator Γ μ is bounded, determine the exact value of the norm for p ≥ 4 , and provide norm estimates for the other values of p . Additionally, we observe an unexpected behavior in the case p = 2 . Finally, we characterize the measures μ for which Γ μ is compact by calculating its exact essential norm.
Bellavita et al. (Mon,) studied this question.