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Duality of a pair of spaces of analytic functions of bounded growth. (English. Russian original) Zbl 0776.32005
Sov. Math., Dokl. 44, No. 1, 314-317 (1992); translation from Dokl. Akad. Nauk SSSR 319, No. 6, 1297-1300 (1991).
Given a decreasing sequence $$\{\varphi_ n\}$$ of finite, nonnegative, convex functions on a bounded convex domain $$D\subset\mathbb{C}^ n$$, the author considers the space of all analytic functions $$y(z)$$ such that $$\sup_ D| y(z)| e^{-\varphi_ n(z)}<\infty$$. A description of dual space is presented.

##### MSC:
 32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) 32C37 Duality theorems for analytic spaces
##### Keywords:
spaces of analytic functions; bounded growth; dual space