Removable singularities in the Nevanlinna class and in the Hardy classes

Abstract

We show that certain sets in C n , n ≥ 2 {{\mathbf {C}}^n},n \geq 2 , which we call n n -small, are removable singularities for holomorphic functions in the Nevanlinna class. Since our class of sets includes polar sets (in R 2 n {{\mathbf {R}}^{2n}} ) our result includes the previous removable singularity results for the Nevanlinna class. We give also a related result for a subclass of the Hardy class.