Topological properties of the Fréchet space of holomorphic functions of several complex variables

Abstract

Let 𝑁p(𝐵n) (𝑝 > 1) be the Privalov class of holomorphic functions on the unit ball 𝐵n in the space of 𝑛-complex variables. The class 𝑁p(𝐵n) (𝑝 > 1), equipped with the topology given by a natural metric, becomes an 𝐹-algebra. In this paper, we shall introduce a Fréchet space Fp(𝐵n) (𝑝 > 1) of holomorphic functions on 𝐵n which contains 𝑁p(𝐵n). Moreover, we shall characterize some topological properties of Fp(𝐵n) induced by the family of semi norms on Fp(𝐵n) .