The Cauchy-Riemann equations on product domains

Debraj Chakrabarti, Mei Chi Shaw

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


We establish the L2 theory for the Cauchy-Riemann equations on product domains provided that the Cauchy-Riemann operator has closed range on each factor. We deduce regularity of the canonical solution on (p, 1)-forms in special Sobolev spaces represented as tensor products of Sobolev spaces on the factors of the product. This leads to regularity results for smooth data.

Original languageEnglish
Pages (from-to)977-998
Number of pages22
JournalMathematische Annalen
Issue number4
StatePublished - Apr 2011


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