Interpolating Sequences for the Nevanlinna and Smirnov Classes
نویسنده
چکیده
We give analytic Carleson-type characterisations of the interpolating sequences for the Nevanlinna and Smirnov classes. From this we deduce necessary and sufficient geometric conditions, both expressed in terms of a certain non-tangential maximal function associated to the sequence. Some examples show that the gap between the necessary and the sufficient conditions cannot be covered. We also discuss the relationship between our results and the previous work of Naftalevič for the Nevanlinna class, and Yanagihara for the Smirnov class. Finally, we observe that the arguments used in the previous proofs show that interpolating sequences for “big” HardyOrlicz spaces are in general different from those for the scale included in the classical Hardy spaces.
منابع مشابه
Interpolation and harmonic majorants in big Hardy-Orlicz spaces
Free interpolation in Hardy spaces is characterized by the well-known Carleson condition. The result extends to Hardy-Orlicz spaces contained in the scale of classical Hardy spaces H, p > 0. For the Smirnov and the Nevanlinna classes, interpolating sequences have been characterized in a recent paper in terms of the existence of harmonic majorants (quasi-bounded in the case of the Smirnov class)...
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Free interpolation in Hardy spaces is caracterized by the well-known Carleson condition. The result extends to Hardy-Orlicz spaces contained in the scale of classical Hardy spaces H, p > 0. For the Smirnov and the Nevanlinna classes, interpolating sequences have been characterized in a recent paper in terms of the existence of harmonic majorants (quasi-bounded in the case of the Smirnov class)....
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