Let mu be a positive Borel measure on the interval 0,1). Suppose H-mu is the Hankel matrix (mu(n,k))(n,k >= 0) with entries mu(n,k) = mu(n+k), where mu(n) = integral(0,1)) t(n)d mu(t). The matrix formally induces the operator H-mu(f)(z) = Sigma(infinity)(n=0) (Sigma(infinity)(k=0) mu(n),(k) a(k))z(n), which has been widely studied in Bao and Wulan (J Math Anal Appl 409:228-235, 2014), Chatzifountas et al. (JMath Anal Appl 413:154-168, 2014), Galanopoulos and Pelaez (Stud Math 200:201-220, 2010) and Girela and Merchan (Banach JMath Anal 12:374-398, 2018). In this paper, we define the Derivative-Hilbert operator as
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