Separately harmonic and subharmonic functions

A uniform boundedness principle in pluripotential theory

“…(Separately subharmonic means that (2) holds just with lines L parallel to the coordinate axes.) Further results along these lines were obtained in [1,5,7]. -Wiegerinck [11] gave an example of a separately subharmonic function that is not upper semicontinuous.…”

Subharmonic functions, generalizations, weighted boundary behavior, and separately subharmonic functions: A survey

“…For results on this area, see e.g. [46,25,43,47,42,48,49,41,50,51,4], and the references therein. We consider here a result of Arsove, Theorem 4A, and a result of Kołodziej and Thorbiörnson, Theorem 4B.…”