Analytic Description of the Spaces Dual to Spaces of Holomorphic Functions of Given Growth on Carathéodory Domains

On space of holomorphic functions with boundary smoothness and its dual

“…In view of Condition 𝑖 3 ), the space 𝐴 𝑚+1 (Ω) is continuously embedded into 𝐴 𝑚 (Ω) for each 𝑚 ∈ N. It is clear that 𝐴 ℋ (Ω) is a Frechét space continuously embedded into 𝐴 ∞ (Ω), and by Condition 𝑖 4 ), it is invariant with respect to the differentiation. The spaces of holomorphic functions with a boundary smoothness naturally arise in studying many problems in complex analysis, operator theory, approximation theory [1]- [9]. It is clear that for each 𝑧 ∈ C 𝑛 the function 𝑓 𝑧 (𝜆) = 𝑒 ⟨𝜆,𝑧⟩ belongs to 𝐴 ∞ (Ω).…”