The Cauchy-Riemann equations on product domains

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.

Some typos fixed

Cited by in corpus (2)

• $L^2$ Serre Duality on Domains in Complex Manifolds and Applications
• Spectrum of the complex Laplacian on product domains