Integration operators on Bergman spaces
Let ${\bold D}$ denote the unit disk in the complex plane and let $m$ be the area Lebesgue measure on ${\bold D}$. Given a positive integrable function $w$ (a weight) on ${\bold D}$, let $L^p_{\rm a}(w)$ denote the collection of analytic functions $f$ on ${\bold D}$ such that $|f|^pw$ is integrable. Given an analytic function $g$ on ${\bold D}$, the operator $T_g$ is defined by $T_g f(z) = \int_