on the L 2 -dolbeault cohomology of annuli

Debraj Chakrabarti, Christine Laurent-Thiébaut, Mei Chi Shaw

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


For certain annuli in C n , n á 2, with non-smooth holes, we show that the ∂ s -operator from L 2 functions to L 2 (0, 1)-forms has closed range. The holes admitted include products of pseudoconvex domains and certain intersections of smoothly bounded pseudoconvex domains. As a consequence, we obtain estimates in the Sobolev space W 1 for the ∂ s -equation on the non-smooth domains which are the holes of these annuli.

Original languageEnglish
Pages (from-to)831-857
Number of pages27
JournalIndiana University Mathematics Journal
Issue number2
StatePublished - 2018


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