Essential norms of integral operators on spaces of analytic functions (Q435093)

The authors investigate the essential norms of integral operators on some Banach spaces of analytic functions on the unit disk \(\mathbb D\) in the complex plane. They investigate operators of the form NEWLINE\[NEWLINE (I_{g}f)(z)=\int_{0}^{z}f'(w)g(w)\,dw,\quad z\in {\mathbb D}, NEWLINE\]NEWLINE and NEWLINE\[NEWLINE (T_{g}f)(z)=\int_{0}^{z}f(w)g'(w)\,dw,\quad z\in {\mathbb D}. NEWLINE\]NEWLINE They find boundedness conditions for the norm and the essential norm for \(I_{g}\) in the cases of a Bloch space, a Dirichlet space and a BMOA space. In the case of \(T_{g}\) and some spaces of analytic functions, they obtain two-sided estimates for the essential norm. They also investigate the essential norm of the little Hankel operator.