## 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

Zbl 1068.30027
Full Text:

### References:

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