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Domination conditions for families of quasinearly subharmonic functions. (English) Zbl 1220.31007
Summary: Y. Domar [Ark. Mat. 3, 429–440 (1958; Zbl 0078.09301)] has given a condition that ensures the existence of the largest subharmonic minorant of a given function. Later, P. J. Rippon [Math. Scand. 49, 128–132 (1981; Zbl 0472.31002)] pointed out that a modification of Domar’s argument gives in fact a better result. Using our previous, rather general and flexible, modification of Domar’s original argument, we extend their results both to the subharmonic and quasinearly subharmonic settings.
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
31C45 Other generalizations (nonlinear potential theory, etc.)
Full Text: DOI arXiv
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