A Carleson estimate for the complex Monge–Ampère operator

Mats Andersson

Vol. 184 (1998), No. 2, 201–205

DOI: 10.2140/pjm.1998.184.201

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.

Milestones

Received: 7 November 1996

Revised: 12 February 1997

Published: 1 June 1998