A DERIVATIVE-HILBERT OPERATOR ACTING FROM BESOV SPACES INTO BLOCH SPACE

If mu is a positive Borel measure on the interval [0,1), we let H-mu be the Hankel matrix H-mu= (mu(n,k))(n,k >= 0) with entries mu(n,k) = mu(n+k) and mu(n) = integral([0,1)) t(n)d mu (t). Using H-mu , Ye and Zhou first defined the Derivative-Hilbert operator as D H-mu(f)(z) = Sigma(infinity)(n=0) (Sigma(infinity)(k=0) mu(n,k)a(k)) (n+1)z(n), z is an element of D, k=0 where f (z) = Sigma(infinity)(n=0) a(n)z(n) is an analytic function in D. In this paper, we characterize the measure mu for which DH mu is a bounded (resp., compact) operator from Besov space B-p into Bloch space B with 1 < p < infinity.