On Semisubmedian Functions and Weak Plurisubharmonicity

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DOI:

https://doi.org/10.4067/S0719-06462010000200015

Abstract

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.

Keywords

Subharmonicity , seminear subharmonicity , Jensen function , weak subharmonicity , weak plurisubharmonicity
  • Chia-chi Tung Department of Mathematics and Statistics, Minnesota State University, Mankato, Mankato, MN 56001, USA.
  • Pages: 235–259
  • Date Published: 2010-06-01
  • Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal

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Published

2010-06-01

How to Cite

[1]
C.- chi Tung, “On Semisubmedian Functions and Weak Plurisubharmonicity”, CUBO, vol. 12, no. 2, pp. 235–259, Jun. 2010.