Concerning the energy class E_pfor 0<p<1

Weighted Pluricomplex Energy

“…5.1. In particular, this provides a simple proof of the U. Cegrell's main theorem in [11]for p ≥ 1 and in [1] for 0 < p ≤ 1.…”

Modulability and duality of certain cones in pluripotential theory

“…For p 1, Theorem 4.1 was proved in [33] (see also [12,15]), and for 0 < p < 1 in [3]. If p = 0, then (4.1) can be interpreted as Corollary 5.6 in [13].…”

“…As an application of this decomposition theorem we obtain an estimate of the modular constant for the functions in this decomposition, both in l 2 -and l ∞ -norm (Corollary 6. 3). An application of Theorem 6.2 is that δE p (Ω)…”

“…Let p > 0, then E p is defined to be the family of all negative plurisubharmonic functions with well-defined, and finite, pluricomplex p-energy. These cones were introduced and studied in [12] (see also [3,15,21,33]). It is not only within pluripotential theory these cones have been proven useful, but also as a tool in dynamical systems and algebraic geometry (see e.g.…”

On the Cegrell classes

“…The set {z ∈ : ϕ k j (z) < −(j + 1) 3 } is open and dd c ϕ j n converges in the weak * -topology to (dd c v) n and therefore it follows for large l j > k j that…”