A mean value criterion for plurisubharmonic functions

Rakhimov, Karim; Shopulatov, Shomurod

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Pré-publication ou Document de travail

Title :

A mean value criterion for plurisubharmonic functions

Author(s) :

Rakhimov, Karim [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Centre National de la Recherche Scientifique [CNRS]
Shopulatov, Shomurod [Auteur]
National University of Uzbekistan

HAL domain(s) :

Mathématiques [math]/Variables complexes [math.CV]

English abstract : [en]

In this paper we prove a criterion for plurisubharmonic functions in terms of integral mean by complex ellipsoids. Moreover, by using the criterion we prove an analogue of Blaschke-Privalov theorem for plurisubharmonic ...
Show more >In this paper we prove a criterion for plurisubharmonic functions in terms of integral mean by complex ellipsoids. Moreover, by using the criterion we prove an analogue of Blaschke-Privalov theorem for plurisubharmonic functions. 11-LABX-0007-01) managed by the Agence Nationale de la Recherche. 2. Integral criterion for psh functions Let us recall the definition of psh functions. Definition 2.1. Let D ⊂ C n be a domain. An upper semi-continuous function u : D → [−∞, ∞), is called plurisubharmonic in D (shortly u(z) ∈ psh(D)) if for any complex line l the function u| l is subharmonic in l ∩ D. Now we show the construction of a new integral criterion for psh functions. Let us state the first main proposition of this sectionShow less >

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Laboratoire Paul Painlevé - UMR 8524

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