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 = [0,1) t n dµ(t), induces formally the operator(1−tz) 2 dµ(t) for all in Hardy spaces H p (0 < p < ∞), and among them we describe those for which DH µ is a bounded(resp.,compact) operator from H p (0 < p < ∞) into H q (q > p and q ≥ 1). We also study the analogous problem in Hardy spaces H p (1 ≤ p ≤ 2).

Let µ be a positive Borel measure on the interval [0,1). For β > 0, The generalized Hankel matrixon the space of all analytic function f (z) = ∞ k=0 a k z n in the unit disc D. In this paper, we characterize those positive Borel measures on [0, 1) such that H µ,β (f )(z) = [0,1)for all in weighted Bergman Spaces A p α (0 < p < ∞, α > −1), and among them we describe those for which H µ,β (β > 0) is a bounded(resp.,compact) operator on weighted Bergman spaces and Dirichlet spaces.

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