Quasi-Nearly Subharmonic Functions and Quasiconformal Mappings

Abstract

We prove that the composition of a quasi-nearly subharmonic function and a quasiregular mapping of bounded multiplicity is quasi-nearly subharmonic. Also, we prove that if u ∘ f is quasi-nearly subharmonic for all quasi-nearly subharmonic u and f satisfying some additional conditions, then f is quasiconformal. Similar results are further established for the class of regularly oscillating functions.