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

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• 作者：Mehmet ?eli?k ; S?nmez ?ahuto?lu
• 关键词：&part ; ¯ ; -Neumann operator ; Hankel operators ; Bergman projection ; Pseudoconvex domain
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2014
• 出版时间：1 January, 2014
• 年：2014
• 卷：409
• 期：1
• 页码：393-398
• 全文大小：383 K

文摘

Let be a bounded pseudoconvex domain in , and . We show that compactness of the -Neumann operator, , on square integrable -forms is equivalent to compactness of the commutators on square integrable -closed -forms for where is the Bergman projection on -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.