The Cauchy-Riemann equations on product domains

Debraj Chakrabarti; Mei-Chi Shaw

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arXiv · 0911.0103

The Cauchy-Riemann equations on product domains

Debraj Chakrabarti·Mei-Chi Shaw

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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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BibTeX RIS

Debraj Chakrabarti, Mei-Chi Shaw. 2010-05-10. The Cauchy-Riemann equations on product domains. https://arxiv.org/abs/0911.0103

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