Abstract
The main purpose of this paper is to introduce and study the notion of -maximal \(\mathcal {F}\)-plurisubharmonic functions, which extends the notion of maximal plurisubharmonic functions on a Euclidean domain to an -domain of ℂ n in a natural way. Our main result is that a finite -plurisubharmonic function u on a plurifine domain U satisfies (d d c u)n= 0 if and only if u is -locally -maximal outside some pluripolar set. In particular, a finite -maximal plurisubharmonic function u satisfies (d d c u)n = 0.
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El Kadiri, M., Smit, I.M. Maximal Plurifinely Plurisubharmonic Functions. Potential Anal 41, 1329–1345 (2014). https://doi.org/10.1007/s11118-014-9421-x
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DOI: https://doi.org/10.1007/s11118-014-9421-x