LOCALIZATION OF COMPACTNESS OF HANKEL OPERATORS ON PSEUDOCONVEX DOMAINS

摘要

We prove the following localization for compactness of Hankel operators on Bergman spaces. Assume that Ω is a bounded pseudoconvex domain in C~n, p is a boundary point of Ω, and B(p, r) is a ball centered at p with radius r so that U = Ω ∩ B(p,r) is connected. We show that if the Hankel operator H~Φ_Ω with symbol Φ ∈ C~1(Ω) is compact on A~2(Ω) then H_R_U~U(Φ) is compact on A~2(U) where R_U denotes the restriction operator on U, and A~2(Ω) and A~2(U) denote the Bergman spaces on Ω and U, respectively.