HARTMANN, Andreas; MASSANEDA, Xavier; NICOLAU, Artur; THOMAS, Pascal J.

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HARTMANN, Andreas
Institut de Mathématiques de Bordeaux [IMB]

MASSANEDA, Xavier

NICOLAU, Artur

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J. Funct. Anal. 217. 2004, vol. 217, p. 1-37

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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.< Leer menos

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free interpolation

Smirnov and Nevanlinna class

harmonic majorants

Poisson balayage

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Interpolation in the Nevanlinna and Smirnov classes and harmonic majorants

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