Localization of compactness of Hankel operators on pseudoconvex domains

Details Localization of compactness of Hankel operators on pseudoconvex domains Localization of compactness of Hankel operators on pseudoconvex domains

2011-10-09

arxiv.org/abs/1110.1823v1

Mathematics

Complex Variables

9 pages. To appear in Illinois J. Math

Scientific paper

We prove the following localization for compactness of Hankel operators on Bergman spaces. Assume that D is a bounded pseudoconvex domain in C^n, p is a boundary point of D and B(p,r) is a ball centered at p with radius r so that U=D\cap B(p,r) is connected. We show that if the Hankel operator H^D_f is compact on A^2(D) (the symbols f is C^1 on the closure of D) then H^U_f is compact on A^2(U) where A^2(D) and A^2(U) denote the Bergman spaces on D and U, respectively.

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