

Seminar on Complex Analysis (Gonchar Seminar)
December 2, 2013 18:00, Moscow, Steklov Mathematical Institute, Room 411 (8 Gubkina)






Mean value type inequalities for quasinearly subharmonic functions
A. A. Dovgoshey^{} ^{} Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk

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Abstract:
The mean value type inequality is characteristic for upper semicontinuous functions to be subharmonic.
Quasinearly subharmonic functions generalize subharmonic functions. The necessary and sufficient conditions
under which subsets of balls are “big enough” for the characterization of nonnegative, quasinearly subharmonic
functions by mean value inequalities are found. Similar result is obtained also for generalized mean value
inequalities where, instead of balls, we consider arbitrary bounded sets, which have nonvoid interiors and
instead of the volume of ball some functions depending on the diameter of considering set.

