A generalized Hilbert matrix acting on Hardy spaces

If μ   is a positive Borel measure on the interval [0,1)[0,1), the Hankel matrix Hμ=(μn,k)n,k⩾0Hμ=(μn,k)n,k⩾0 with entries μn,k=∫[0,1)tn+kdμ(t) induces formally the operatorHμ(f)(z)=∑n=0∞(∑k=0∞μn,kak)zn on the space of all analytic functions f(z)=∑k=0∞akzk, in the unit disc DD. In this paper we describe those measures μ   for which HμHμ is a bounded (compact) operator from HpHp into HqHq, 0