Pluripolar sets and the subextension in Cegrell's classes

Abstract

In this article, we prove that if E is a complete pluripolar set in , then E ¼ {' ¼ À1} for some ' 2 F 1 (). Moreover, we study the subextension in Cegrell's class E p .

Weak solutions to the complex Monge-Ampere equation on open subsets of $\mathbb{C}^n$

“…Proof. By Lemma 4.5 in [17] we haveû ∈ F(Ω) and (dd cû ) n ≤ 1 Ω (dd c u) n inΩ. Since (dd c u) n is carried by a pluripolar set of Ω, Theorem 5.11 in [9] implies that (dd c u)…”

Subextension of plurisubharmonic functions with boundary values in weighted pluricomplex energy classes

“…He proved in [3] that if ⊂ C n are bounded hyperconvex domains and u ∈ E p ( ), then there exists a function u ∈ E p ( ) such that u ≤ u on and…”

Some Weighted Energy Classes of Plurisubharmonic Functions

“…Namely, in Theorem 3.1 of Section 3 by relying on Theorem C of Kolodziej in [18], we show that under certain conditions the class E χ ( ) is contained in E( ) or N ( ). It should be remarked that our Theorem 3.1 is more general than Proposition A in [5] and that the class E χ ( ) in the case χ(t) = min(|t| p , 1), t < 0 has been introduced earlier in [15]. Weighted energy classes of plurisubharmonic functions on compact Kahlër manifolds also have been studied in [12] recently.…”