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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.12 no.2 Temuco  2010

http://dx.doi.org/10.4067/S0719-06462010000200015 

CUBO A Mathematical Journal Vol.12, N° 02, (235–259). June 2010

 

On Semisubmedian Functions and Weak Plurisubharmonicity

Chia-chi Tung1

Dept. of Mathematics and Statistics, Minnesota State University, Mankato, Mankato, MN 56001, USA email: chia.tung@mnsu.edu


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.

Key words and phrases: Subharmonicity, seminear subharmonicity, Jensen function, weak subharmonicity, weak plurisubharmonicity


RESUMEN

En esta nota son estudiadas intrínsicamente las funciones subarmonicas y plurisubarmonicas sobre un espacio complejo. Para aplicaciones, subarmonicidad es caracterizada mas eficientemente en términos de propiedades que necesitan ser verificadas solamente localmente en un subconjunto analítico delgado; estas aplicaciones incluyen la desigualdad del valor-submedio, la monotonicidad esférica (respectivamente, sólida), bien como subarmonicidad debil. Varios resultados de Gunning [9, K and L] son extendibles vía regularidad a espacios complejos. En particular, plurisubarmonicidad (sobre un espacio normal) importa esencialmente para plurisubarmonicidad débil regularizada y similarmente para subarmoniciada (sobre un espacio general). Son dados un lema de Hartogs generalizado y un criterio de constancia para ciertas aplicaciones matriz-valuada.

2000 Math. Subj. Class.: Primary: 31C05; Secondary: 31C10, 32C15


Notas

1Supports by the ”Globale Methoden in der komplexen Geometrie” Grant of the German research society DFG and the Faculty Improvement Grant of Minnesota State University, Mankato, are gratefully acknowledged.

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Received: January 2009.

Revised: May 2009.