Bi-Lipschitz Mappings and Quasinearly Subharmonic Functions

After considering a variant of the generalized mean value inequality of quasinearly subharmonic functions, we consider certain invariance properties of quasinearly subharmonic functions. Kojić has shown that in the plane case both the class of quasinearly subharmonic functions and the class of regularly oscillating functions are invariant under conformal mappings. We give partial generalizations to her results by showing that inℝn,n≥2, these both classes are invariant under bi-Lipschitz mappings.