Let D be a pseudoconvex
domain in ℂn that admits a plurisubharmonic defining function ρ of class C2.
We prove that if u1,…,ur are bounded plurisubharmonic functions in D
and ω = ddc log 1∕(−ρ), then (−ρ)nddcu1 ∧… ∧ ddcur ∧ ωn−r∕(n − r)! is a
Carleson measure. This is a global variant of the Chern-Levine-Nirenberg
inequality.
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