Family of Subharmonic Functions and Separately Subharmonic Functions

2016/05/31 by Kalantar, Mansour
#31B05 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.09754

Abstract

We prove that the upper envelope of a family of subharmonic functions defined on an open subset of ℝ^N, (N≥2), that is finite every where, is locally bounded above outside a closed nowhere dense set with no bounded components. Then we conclude as a consequence that a separately subharmonic function is subharmonic outside a closed nowhere dense set with no bounded components. It generalizes a result due to Cegrell and Sadullaev.

Related

• Uniqueness theorems for subharmonic functions
• Liouville-type theorems with constraints outside of small sets on circles or spheres for functions of finite order
• Lower envelopes with respect to convex subcones of subharmonic and plurisubharmonic functions
• Separately Subharmonic and Harmonic Functions are Subharmonic
• Restricted Perron envelopes and quasibounded functions