For 0 < p < ∞, the Bergman space L_a~p consists of those functions f analytic in the unit disk D = { z ∈ C : |z| < 1 } for which ||f||_(L_a~p)~p = ∫∫_D|f(z)|~p(dA(z))/π < ∞. If p ≥ 1 then || • || L_a~p is a norm making L_a~p a Banach space, and if 0 < p < 1 then d(f, g) = ||f — g||_(L_a~p)~p is a metric making L_a~p a nonlocally convex complete metric topological vector space.
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机译：对于0 <∞，Bergman空间L_a〜p由在单元盘D = {z∈C：| z |中解析的那些函数f组成。 <| 1 | || f || _（L_a〜p）〜p =∫∫_D| f（z）|〜p（dA（z））/π<∞。如果p≥1，则|| •|| L_a〜p是建立L_a〜pa Banach空间的范数，如果0 <1，则d（f，g）= || f — g || _（L_a〜p）〜p是形成L_a〜pa的度量非局部凸完整度量拓扑向量空间。
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