A mean value criterion for plurisubharmonic functions

Karim Rakhimov (1, 2) , Shomurod Shopulatov (3)

1 CNRS - Centre National de la Recherche Scientifique
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 National University of Uzbekistan

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 section

Domaines: Variables complexes [math.CV]

Karim Rakhimov, Shomurod Shopulatov. A mean value criterion for plurisubharmonic functions. 2021. ⟨hal-03233153⟩