On Semisubmedian Functions and Weak Plurisubharmonicity

• Chia-chi Tung ^[1]
  1. [1] Minnesota State University Dept. of Mathematics and Statistics
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 12, Nº. 2, 2010, págs. 235-259
• Idioma: inglés
• DOI: 10.4067/S0719-06462010000200015
• Enlaces
  • Texto completo
• Resumen
  • español

    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.

  • English

    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.

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