Interpolation in the Nevanlinna and Smirnov classes and harmonic majorants

Andreas Hartmann (1) , Xavier Massaneda , Artur Nicolau , Pascal J. Thomas (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We consider a free interpolation problem in Nevanlinna and Smirnov classes and find a characterization of the corresponding interpolating sequences in terms of the existence of harmonic majorants of certain functions. We also consider the related problem of characterizing positive functions in the disk having a harmonic majorant. An answer is given in terms of a dual relation which involves positive measures in the disk with bounded Poisson balayage. We deduce necessary and sufficient geometric conditions, both expressed in terms of certain maximal functions.

Mots clés: free interpolation; Smirnov and Nevanlinna class; harmonic majorants; Poisson balayage

Domaines: Variables complexes [math.CV]

Andreas Hartmann, Xavier Massaneda, Artur Nicolau, Pascal J. Thomas. Interpolation in the Nevanlinna and Smirnov classes and harmonic majorants. J. Funct. Anal. 217, 2004, 217, pp.1-37. ⟨hal-00128477⟩