Bi-Lipschitz Mappings and Quasinearly Subharmonic Functions: Advanced Study

After considering a variant of the generalized mean value inequality of quasi-nearly subharmonic
functions, we consider certain invariance properties of quasinearly subharmonic functions. Koji´c
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 of these results by showing that in Rn, n ≥ 2, these both classes are invariant under
bi-Lipschitz mappings.

Author (s) Details

Oleksiy Dovgoshey
Department of Theory of Functions, Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, 84100, Slovyansk, Ukraine.

Juhani Riihentaus
Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FI-90014 Oulun Yliopisto, Finland and Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland.

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