On compactness of the ∂-Neumann operator on Hartogs domains

2018/08/21 by Jin, Muzhi
#32W05 #32W10 #47B35 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.06948

Abstract

We show that Property (P) of ∂Ω, compactness of the ∂-Neumann operators N₁, and compactness of Hankel operator on a smooth bounded pseudoconvex Hartogs domain Ω=\(z, w₁, w₂,…, w_n) ∈ ℂⁿ⁺¹ |∑_k=1ⁿ |w_k|² < e^-2φ(z), z\inD\ are equivalent, where D is a smooth bounded connected open set in ℂ.

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