Localization of compactness of Hankel operators on pseudoconvex domains
Complex Variables
2021-03-08 v1 Functional Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.1110.1823,
title = {Localization of compactness of Hankel operators on pseudoconvex domains},
author = {Sonmez Sahutoglu},
journal= {arXiv preprint arXiv:1110.1823},
year = {2021}
}
Comments
9 pages. To appear in Illinois J. Math