A note on interpolation in the Lumer’s Nevanlinna class. (English) Zbl 1143.32004

Duong Ngoc Son

Indag. Math., New Ser. 18, No. 3, 447-453 (2007).

Let \(X\) be a space of holomorphic functions in \(\mathbb{B}_n\), the unit ball of \(\mathbb{C}^n\). A sequence \(a= \{a_k\}_{k\geq 1}\) is said to be free interpolating for \(X\) if \(\{w_k a_k\}_k\in X|_a\) for every \(\{\alpha_k\}_k\in X|_a\) and every bounded sequence \(\{w_k\}_k\).
A. Hartmann, X. Massaneda, A. Nicolau and P. Thomas characterized the free interpolating sequences for the Nevanlinna class \(N\) of the disk in terms of harmonic majorants, and described the trace \(N|_a\) [J. Funct. Anal. 217, No. 1, 1–37 (2004; Zbl 1068.30027)].
In the present paper the author obtains similar results for Lumer’s Nevanlinna class \(LN(\mathbb{B}_n)\), consisting of all the holomorphic functions \(f\) such that \(\log^+|f|\) admits a pluriharmonic majorant.

Reviewer: Daniel Suárez (Barcelona)

MSC:

32A36	Bergman spaces of functions in several complex variables
30H05	Spaces of bounded analytic functions of one complex variable

Keywords:

free interpolation; Lumer’s Nevanlinna class; pluriharmonic majorants

Citations:

Zbl 1068.30027

References:

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