Bergman Space

Let  be an open subset of the complex plane , and let  denote the collection of all analytic functions  whose complex modulus is square integrable with respect to area measure. Then , sometimes also denoted , is called the Bergman space for . Thus, the Bergman space consists of all the analytic functions in . The Bergman space can also be generalized to , where .

REFERENCES:

Hedenmalm, H.; Korenblum, B.; and Zhu, K. Theory of Bergman Spaces. New York: Springer-Verlag, 2000.

Shields, A. L. "Weighted Shift Operators and Analytic Function Theory." In Topics in Operator Theory (Ed. C. Pearcy). Providence, RI: Amer. Math. Soc., pp. 49-128, 1979.

Zhu, K. Operator Theory in Function Spaces. New York: Dekker, 1990.