A Derivative-Hilbert operator acting on Bergman spaces

The range of Hilbert operator and Derivative-Hilbert operator acting on $H^1$

“…Ye and Zhou characterized the measure µ for which I µ 2 and DH µ is bounded (resp.,compact) on Bloch space in [18]. They did the similar researches on Bergman spaces in [19]. In [6], Bao and Wulan gave another description about Carleson measure on [0, 1) and proved that when 0 < p < 2, the range of the cesàro-like operator acting on H ∞ is a subset of Q p if and only if µ is a Carleson measure.…”

“…on the space of analytic functions in D. The Derivative-Hilbert operator DH µ is first studied by Ye and Zhou [18,19], they defined DH µ as…”

Hilbert-type operators acting between weighted Fock spaces

“…During the last two decades, the Hilbert operator H and its generalizations defined on various spaces of holomorphic functions on the unit disk D in C have been much investigated. See, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13], [15], [17], [18].…”

“…Proof of "only if" part of Theorem 1.2. In our proof, we need the following well-known estimate, see [18,Page 54]. Let 0 < w < 1.…”

A Derivative-Hilbert operator acting on Hardy spaces

“…whenever the right hand side makes sense and defines an analytic function in D. We can easily see that the case α = 1 is the integral representation of the generalized Hilbert operator. Ye and Zhou characterized the measure µ for which Iµ 2 and DH µ is bounded (resp.,compact) on Bloch space [16] and Bergman spaces [17].…”