Geodesic
MEAN VALUE TYPE INEQUALITIES FOR QUASINEARLY SUBHARMONIC FUNCTIONS
Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 349-368

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DOI

The mean value inequality is characteristic for upper semi-continuous functions to be subharmonic. Quasinearly subharmonic functions generalise subharmonic functions. We find the necessary and sufficient conditions under which subsets of balls are big enough for the characterisation of non-negative, quasinearly subharmonic functions by mean value inequalities. Similar result is obtained also for generalised mean value inequalities where, instead of balls, we consider arbitrary bounded sets, which have non-void interiors and instead of the volume of ball some functions depending on the radius of this ball.
DOI : 10.1017/S0017089512000602
Mots-clés : Primary 31B05, 31C05, Secondary 31C45 
DOVGOSHEY, OLEKSIY; RIIHENTAUS, JUHANI. MEAN VALUE TYPE INEQUALITIES FOR QUASINEARLY SUBHARMONIC FUNCTIONS. Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 349-368. doi: 10.1017/S0017089512000602
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     author = {DOVGOSHEY, OLEKSIY and RIIHENTAUS, JUHANI},
     title = {MEAN {VALUE} {TYPE} {INEQUALITIES} {FOR} {QUASINEARLY} {SUBHARMONIC} {FUNCTIONS}},
     journal = {Glasgow mathematical journal},
     pages = {349--368},
     year = {2013},
     volume = {55},
     number = {2},
     doi = {10.1017/S0017089512000602},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000602/}
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