Bergman Space

Let $G$ be an open subset of the Complex Plane $\Bbb{C}$, and let $L_a^2(G)$ denote the collection of all Analytic Functions $f:G\to C$ whose Modulus is square integrable with respect to Area measure. Then $L_a^2(G)$, sometimes also denoted $A^2(G)$, is called the Bergman space for $G$. Thus, the Bergman space consists of all the Analytic Functions in $L^2(G)$. The Bergman space can also be generalized to $L_a^p(G)$, where $0<p<\infty$.