zbMATH — the first resource for mathematics

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.

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