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For analytic functions  g  on the unit disk with non-negative Maclaurin coefficients, we describe the boundedness and compactness of the integral operator    $$T_g(f)(z)=\int _0^zf(\zeta )g'(\zeta )\,d\zeta $$  T g ( f ) ( z ) = ∫ 0 z f ( ζ ) g ′ ( ζ ) d ζ from a space  X  of analytic functions in the unit disk to    $$H^\infty $$  H ∞ , in terms of neat and useful conditions on the Maclaurin coefficients of  g . The choices of  X  that will be considered contain the Hardy and the Hardy–Littlewood spaces, the Dirichlet-type spaces    $$D^p_{p-1}$$  D p - 1 p , as well as the classical Bloch and    $$\mathord {\mathrm{BMOA}}$$  BMOA spaces.

Integral Operators Induced by Symbols with Non-negative Maclaurin Coefficients Mapping into $$H^\infty $$