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

In this paper we establish a relation between classes of ω-plurisubharmonic functions \(\mathcal{E}_{p}(X,\omega), p>0\) 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 Kahler manifold X. We show that \(\mathcal{E}_{n-1}(X,\omega)\subset\mathrm{DMA}_{\mathrm {loc}}(X,\omega)\) but \(\bigcap_{0 < p < n-1}\mathcal{E}_{p}(\mathbb{CP}^{n},\omega)\not \subset\mathrm{DMA}_{\mathrm{loc}}(\mathbb{CP}^{n},\omega)\). At the same time we investigate a relation between the classes \(\mathrm{DMA} (\mathbb{C}^{n})\cap\mathcal{L}(\mathbb{C}^{n})\) and \(\mathrm {DMA}(\mathbb{CP}^{n},\omega)\), as well as \(\widehat{\mathrm{DMA}}(\mathbb{C}^{n})\cap\mathcal {L}(\mathbb{C}^{n})\) and \(\widehat{\mathrm{DMA}}\) \((\mathbb{CP}^{n},\omega)\).