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The Cauchy–Riemann equations on product domains

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Abstract

We establish the L 2 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.

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Authors and Affiliations

  1. Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46556, USA

    Debraj Chakrabarti & Mei-Chi Shaw

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  1. Debraj Chakrabarti
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  2. Mei-Chi Shaw
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Correspondence to Debraj Chakrabarti.

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Chakrabarti, D., Shaw, MC. The Cauchy–Riemann equations on product domains. Math. Ann. 349, 977–998 (2011). https://doi.org/10.1007/s00208-010-0547-x

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  • DOI: https://doi.org/10.1007/s00208-010-0547-x

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