ABSTRACT
To begin, we suppose that Ω is merely a domain in the plane of finite area and we do not make any assumptions about the nature of the boundary. The Bergman space, denoted H2(Ω), is the space of holomorphic functions on Ω that are square integrable on Ω with respect to area measure dA = dx ∧ dy = i2dz ∧ dz¯, i.e., h in H2(Ω) are holomorphic functions such that
∫∫ Ω |h|2 dA < ∞. We may think of H2(Ω) as being a subset
of L2(Ω) by adopting the standard convention that two functions that agree almost everywhere are the same function. Theorem 6.5 shows that H2(bΩ) is a subset of H2(Ω) when the domain is bounded and smooth.
