L^2(C): Functions in the Bergmann Space of Complex C

[Nusc]

Which functions are in L_{a}^{2}(C)? C, complex.

THis is the Bergmann space for C

Isn't this just the collection of all analytic functions for C such that

int int |f(x+iy)|^2 dxdy<infinity ? over C

 

[quasar987]

http://mathworld.wolfram.com/BergmanSpace.html

 

[Nusc]

How do I show which functions are in the bergman space for C using the cauchy inequality?