Acta Mathematica Vietnamica

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On some classes of ω-plurisubharmonic functions on compact Kähler manifolds
Nguyen Van Phu, Vu Viet Hung

 

Abstract

In this paper we establish a relation between classes of ω-plurisubharmonic functions E p (X,ω),p>0   and DMAloc(X,ω)  introduced and investigated by Guedj and Zeriahi (J. Funct. Anal., 250:442–482, 2007) and Cegrell (Acta Math., 180:187–217, 1998; Ann. Inst. Fourier (Grenoble), 54:159–179, 2004), respectively, on a compact Kähler manifold X. We show that E n1 (X,ω)DMA loc (X,ω)    but 0<p<n1 E p (CP n ,ω)/DMA loc (CP n ,ω)      .  At the same time we investigate a relation between the classes DMA (C n )L (C n )      and DMA (CP n ,ω)   , as well as DMA ˆ (C n )L (C n )       and DMA ˆ (CP n ,ω) .

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