Apollon G. Paraskevas

Non-invariance of the Nevanlinna class under the action of the Cesaro and Volterra operators

Using a result of Hayman, we show that the Nevanlinna class of holomorphic functions on the unit disc is not invariant under the action of the Cesaro operator and more generally under the action of Volterra operators on elements g,provided that their derivative's reciprocal belongs to the Nevanlinna class.