Hankel matrices acting on Dirichlet spaces

We give a connection between the Hankel matrix acting on Dirichlet spaces DαDα, 0<α<20<α<2, and the Carleson measure supported on (−1,1)(−1,1). As an application, we prove that the generalized Hilbert operators HβHβ are always bounded on Dirichlet spaces DαDα for 0<α<20<α<2 and that the range (0,2)(0,2) of αα in our results is the best possible.