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On some classes of $ω$ -plurisubharmonic functions on compact Kähler manifolds

$icon-email$ 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 ${DMA}_{loc} (X, ω)$ 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 $$. We show that $E_{n - 1} (X, ω) \subset {DMA}_{loc} (X, ω)$ but $⋂_{0 < p < n - 1} E_{p} ({CP}^{n}, ω) ⊄ {DMA}_{loc} ({CP}^{n}, ω)$ . At the same time we investigate a relation between the classes $DMA (C^{n}) \cap L (C^{n})$ and $DMA ({CP}^{n}, ω)$ as well as $\hat{DMA} (C^{n}) \cap L (C^{n})$ and $\hat{DMA} ({CP}^{n}, ω)$ .

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On some classes of ω-plurisubharmonic functions on compact Kähler manifolds

Abstract

On some classes of $ω$ -plurisubharmonic functions on compact Kähler manifolds