Interpolating sequences for the Nevanlinna and Smirnov classes

Abstract

We give an analytic characterisation of the interpolating sequences for the Nevanlinna and Smirnov classes. From this we deduce a necessary and a sufficient geometric condition, 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 condition cannot be covered. We also discuss the relationship between our results and the previous work of Naftalevic 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'' Hardy-Orlicz spaces are in general different from those for the scale included in the classical Hardy spaces.