Hankel matrices acting on Dirichlet spaces

We give a connection between the Hankel matrix acting on Dirichlet spaces D α , 0 < α < 2 , and the Carleson measure supported on ( − 1 , 1 ) . As an application, we prove that the generalized Hilbert operators H β are always bounded on Dirichlet spaces D α for 0 < α < 2 and that the range ( 0 , 2 ) of α in our results is the best possible.