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arXiv · 1211.5022

Compactness of the dbar-Neumann operator and commutators of the Bergman projection with continuous functions

Mehmet Celik·Sonmez Sahutoglu
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Abstract

Let D be a bounded pseudoconvex domain in $C^n, n\geq 2, 0\leq p\leq n,$ and $1\leq q\leq n-1.$ We show that compactness of the dbar-Neumann operator, $N_{p,q+1},$ on square integrable (p,q+1)-forms is equivalent to compactness of the commutators $[P_{p,q}, \bar{z}_j]$ on square integrable dbar-closed (p,q)-forms for $1\leq j\leq n$ where $P_{p,q}$ is the Bergman projection on (p,q)-forms. We also show that compactness of the commutator of the Bergman projection with functions continuous on the closure percolates up in the dbar-complex on dbar-closed forms and square integrable holomorphic forms.

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Mehmet Celik, Sonmez Sahutoglu. 2012-11-21. Compactness of the dbar-Neumann operator and commutators of the Bergman projection with continuous functions. https://doi.org/10.1016/j.jmaa.2013.07.015

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