m-subharmonic functions on the projective space Pⁿ

Authors

Gokhan Gogus, University Sabanchi, TurkeyFollow
Azimbay Sadullaev, National University of Uzbekistan, Institute of Mathematics of Uzbek Academy, Tashkent, UzbekistanFollow

Abstract

We consider a class of quasi m-subharmonic functions in the projective space ℙⁿ. Similarly to the m-subharmonic functions, we will show a number of potential properties of quasi m-subharmonic functions. We introduce the concepts of Green’s function V_qm^*(z,K,ℙⁿ), ��_m-measure ω_qm^*(z,E,D) and study m-regularities of compact sets K ⊂ ℙⁿ. In contrast to the complex space ℂⁿ, we will prove that in the projective space ℙⁿ the locally m-regularity of compact sets is equivalent to their global m-regularity.

First Page

210

Last Page

220

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Recommended Citation

Gogus, Gokhan and Sadullaev, Azimbay (2021) "m-subharmonic functions on the projective space Pⁿ," Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 4: Iss. 4, Article 7.
DOI: https://doi.org/10.56017/2181-1318.1207