Volterra-type operators mapping weighted Dirichlet space into $$H^\infty $$

Abstract The problem of describing the analytic functions g on unit disc such that integral operator $$T_g(f)(z)=\int _0^zf(\zeta )g'(\zeta )\,d\zeta $$ T g ( f ) z = ∫ 0 ζ ′ d is bounded (or compact) from a Banach space complete metric space) X to Hardy $$H^\infty H ∞ tough problem, and remains unsettled in many cases. For with non-negative Maclaurin coefficients, we describe boundedness compactness $$T_g$$ acting weighted Dirichlet $$D^p_\omega D ω p , induced by an upper doubling weight $$\omega . We also characterize, terms neat conditions weights for which $$T_g: D^p_\omega \rightarrow H^\infty : → only if constant.