Duality of a pair of spaces of analytic functions of bounded growth. (English. Russian original) Zbl 0776.32005

Epifanov, O. V.

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.

Reviewer: A.Pankov (Vinnitsa)

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