  The Hilbert matrix $\mathcal{H}_{n,m} = (n+m+ 1)^{-1}$ has been extensively
studied in previous literature. In this paper we look at generalized Hilbert
operators arising from measures on the interval $[0, 1]$, such that the Hilbert
matrix is obtained by the Lebesgue measure. We provide a necessary and
sufficient condition for these operators to be bounded in $\ell^p$ and
calculate their norm.
