In this note subharmonic and plurisubharmonic functions on a complex space are studied intrinsically. For applications subharmonicity is characterized more effectually in terms of properties that need be verified only locally off a thin analytic subset; these include the submean-value inequalities, the spherical (respectively, solid) monotonicity, near as well as weak subharmonicity. Several results of Gunning [9, K and L] are extendable via regularity to complex spaces. In particular, plurisubharmonicity amounts (on a normal space) essentially to regularized weak plurisubharmonicity, and similarly for subharmonicity (on a general space). A generalized Hartogs’ lemma and constancy criteria for certain matrix-valued mappings are given.
@article{1417,
title = {On Semisubmedian Functions and Weak Plurisubharmonicity},
journal = {CUBO, A Mathematical Journal},
volume = {12},
year = {2010},
language = {en},
url = {http://dml.mathdoc.fr/item/1417}
}
Tung, Chia-chi. On Semisubmedian Functions and Weak Plurisubharmonicity. CUBO, A Mathematical Journal, Tome 12 (2010) . http://gdmltest.u-ga.fr/item/1417/