A DERIVATIVE-HILBERT OPERATOR ACTING ON HARDY SPACES

Let μ be a positive Borel measure on the interval(0,1).The Hankel matrix H_μ=(μ_n,k)_n,k≥0 with entries μ_n,k=μ_n+k,where μ_n=f_[0,1)tⁿdμ(t),induces formally the operator as■,where■ is an analytic function in D.We characterize the positive Borel measures on [0,1) such that DHμ(f)(z)=∫_[0,1),f(t)/((1-tz)²)dμ(t) for all f in the Hardy spaces Hp(0

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