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

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.

MSC:

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

Citations:

Zbl 1068.30027
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References:

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[4] Garnett, J.B., ()
[5] Hartmann, A.; Massaneda, X.; Nicolau, A.; Thomas, P.J., Interpolation in the Nevanlinna and Smirnov classes and harmonic majorants, J. funct. anal, 217, 1-37, (2004) · Zbl 1068.30027
[6] Nikolski, N.K., ()
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