Abstract
Let f and g be analytic on the unit disk \({\mathbb{D}}\). The integral operator T g is defined by \({ T_g f(z) = \int_0^z f(t)g'(t) \,dt, z \in \mathbb{D}}\). The problem considered is characterizing those symbols g for which T g acting on H ∞, the space of bounded analytic functions on \({\mathbb{D}}\), is bounded or compact. When the symbol is univalent, these become questions in univalent function theory. The corresponding problems for the companion operator, \({ S_g f(z)= \int_0^z f'(t)g(t) \,dt}\), acting on H ∞ are also studied.
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Anderson, A., Jovovic, M. & Smith, W. Some integral operators acting on H ∞ . Integr. Equ. Oper. Theory 80, 275–291 (2014). https://doi.org/10.1007/s00020-014-2161-x
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DOI: https://doi.org/10.1007/s00020-014-2161-x