Let G be an open subset of the complex plane C, and let L_a^2(G) denote the collection of all analytic functions f:G->C whose complex 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

Hardy space