Bergman space

Let Gn be a domain and let dV denote the Euclidean volume measure on G.



A2(G):={f holomorpic in G|G|f(z)|2𝑑V(z)<}.

A2(G) is called the Bergman space on G. The norm on this space is defined as


Further we define an inner product on A2(G) as


The inner product as defined above really is an inner product and further it can be shown that A2(G) is completePlanetmathPlanetmathPlanetmath since convergence in the above norm implies normal convergence (uniform convergenceMathworldPlanetmath on compact subsets). The space A2(G) is therefore a Hilbert spaceMathworldPlanetmath. Sometimes this space is also denoted by La2(G).


  • 1 D’Angelo, John P. , CRC Press, 1993.
  • 2 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title Bergman space
Canonical name BergmanSpace
Date of creation 2013-03-22 15:04:43
Last modified on 2013-03-22 15:04:43
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 10
Author jirka (4157)
Entry type Definition
Classification msc 32A36
Related topic BergmanKernel