Some Closed Range Integral Operators On Spaces of Analytic Functions

Abstract

Our main result is a characterization of $g$ for which the operator $S_g(f)(z)={\int }_0^z{f}^{\prime }(w)g(w)dw$ 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 $1\le p<\infty$. We also show the companion operator $T_g(f)(z)={\int }_0^{z}f(w)g^{\prime }(w)dw$ is never bounded below on $H^2$, Bloch, nor BMOA, but may be bounded below on $A^p$.

Cited by in corpus (6)

• Integral operators on analytic Morrey spaces
• Optimal Domain of generalized Volterra operators
• Norm-attaining integral operators on analytic function spaces
• Volterra type operators between Bloch type spaces and weighted Banach spaces
• Volterra type operators on weighted Banach spaces of analytic functions
• Analytic version of critical $Q$ spaces and their properties