  In this note, we frst consider boundedness properties of a family of
operators generalizing the Hilbert operator in the upper triangle case. In the
diagonal case, we give the exact norm of these operators under some
restrictions on the parameters. We secondly consider boundedness properties of
a family of positive Bergman-type operators of the upper-half plane. We give
necessary and sufficient conditions on the parameters under which these
operators are bounded in the upper triangle case.
