The Cauchy-Riemann equations on product domains

Debraj Chakrabarti; Mei-Chi Shaw

The Cauchy-Riemann equations on product domains

Complex Variables 2010-05-11 v2

Authors: Debraj Chakrabarti , Mei-Chi Shaw

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.

Keywords

Cauchy-Riemann equations product domains L^2 theory closed range Sobolev spaces canonical solution

Cite

@article{arxiv.0911.0103,
  title  = {The Cauchy-Riemann equations on product domains},
  author = {Debraj Chakrabarti and Mei-Chi Shaw},
  journal= {arXiv preprint arXiv:0911.0103},
  year   = {2010}
}

Comments

Some typos fixed

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