Hilbert matrix on spaces of Bergman-type

It is well known (see [8,14]) that the Libera operator L is bounded on the Besov space Hνp,q,α if and only if 0<κp,α,ν:=ν−α−1p+1. We prove unexpected results: the Hilbert matrix operator H, as well as the modified Hilbert operator H˜, is bounded on Hνp,q,α if and only if 0<κp,α,ν<1. In particular, H, as well as H˜, is bounded on the Bergman space Ap,α if and only if 1<α+2