# Bergman space

In complex analysis, a branch of mathematics, a **Bergman space**, named after Stefan Bergman, is a function space of holomorphic functions in a domain *D* of the complex plane that are sufficiently well-behaved at the boundary that they are absolutely integrable. Specifically, is the space of holomorphic functions in *D* such that the p-norm

Thus is the subspace of holomorphic functions that are in the space L^{p}(*D*). The Bergman spaces are Banach spaces, which is a consequence of the estimate, valid on compact subsets *K* of *D*:
Template:NumBlk
Thus convergence of a sequence of holomorphic functions in *L*^{p}(*D*) implies also compact convergence, and so the limit function is also holomorphic.

If *p* = 2, then is a reproducing kernel Hilbert space, whose kernel is given by the Bergman kernel.

## References

- {{#invoke:citation/CS1|citation

|CitationClass=citation }}

- {{#invoke:citation/CS1|citation

|CitationClass=citation }}.

- {{#invoke:citation/CS1|citation

|CitationClass=citation }}