The Cauchy-Riemann equations on product domains

Details The Cauchy-Riemann equations on product domains The Cauchy-Riemann equations on product domains

2009-10-31

arxiv.org/abs/0911.0103v2

Mathematics

Complex Variables

Some typos fixed

Scientific paper

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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