Article ID Journal Published Year Pages File Type
4616384 Journal of Mathematical Analysis and Applications 2014 6 Pages PDF
Abstract
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.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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