Abstract
Our main result is a characterization of g for which the operator \({S_g(f)(z) = \int_0^z f'(w)g(w)\, dw}\) is bounded below on the Bloch space. We point out analogous results for the Hardy space H 2 and the Bergman spaces A p for 1 ≤ p < ∞. We also show the companion operator \({T_g(f)(z) = \int_0^z f(w)g'(w) \, dw}\) is never bounded below on H 2, Bloch, nor BMOA, but may be bounded below on A p.
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To Mary Rose
A. Anderson was supported by NSF-DGE-0841223.
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Anderson, A. Some Closed Range Integral Operators on Spaces of Analytic Functions. Integr. Equ. Oper. Theory 69, 87–99 (2011). https://doi.org/10.1007/s00020-010-1827-2
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DOI: https://doi.org/10.1007/s00020-010-1827-2