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Bergman Space

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<p<infty.

See also

Hardy Space

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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.

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Bergman Space

Cite this as:

Weisstein, Eric W. "Bergman Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BergmanSpace.html

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