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

Abstract

AbstractFor 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.