Compactness of the ∂¯-Neumann operator and commutators of the Bergman projection with continuous functions
Let Ω be a bounded pseudoconvex domain in Cn,n≥2,0≤p≤n, and 1≤q≤n−1. We show that compactness of the ∂¯-Neumann operator, Np,q+1, on square integrable (p,q+1)-forms is equivalent to compactness of the commutators [Pp,q,z¯j] on square integrable ∂¯-closed (p,q)-forms for 1≤j≤n where Pp,q is the Bergm...
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Published in | Journal of mathematical analysis and applications Vol. 409; no. 1; pp. 393 - 398 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
01.01.2014
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Subjects | |
Online Access | Get full text |
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Summary: | Let Ω be a bounded pseudoconvex domain in Cn,n≥2,0≤p≤n, and 1≤q≤n−1. We show that compactness of the ∂¯-Neumann operator, Np,q+1, on square integrable (p,q+1)-forms is equivalent to compactness of the commutators [Pp,q,z¯j] on square integrable ∂¯-closed (p,q)-forms for 1≤j≤n where Pp,q is the Bergman projection on (p,q)-forms. We also show that compactness of the commutator of the Bergman projection with bounded functions percolates up in the ∂¯-complex on ∂¯-closed forms and square integrable holomorphic forms. |
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ISSN: | 0022-247X 1096-0813 |
DOI: | 10.1016/j.jmaa.2013.07.015 |