Abstract

Let D be a pseudoconvex domain in Cⁿ that admits a plurisubharmonic defining function ρ of class C². We prove that if u₁,…,u_r are bounded plurisubharmonic functions in D and ω = dd^c log 1 ∕ (−ρ), then (−ρ)ⁿdd^cu₁ ∧…∧dd^cu_r ∧ω^n−r ∕ (n−r)! is a Carleson measure. This is a global variant of the Chern-Levine-Nirenberg inequality.

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