The Cauchy–Riemann equations on product domains
- 27 July 2010
- journal article
- research article
- Published by Springer Science and Business Media LLC in Mathematische Annalen
- Vol. 349 (4), 977-998
- https://doi.org/10.1007/s00208-010-0547-x
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
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This publication has 24 references indexed in Scilit:
- Boundary value problems on Lipschitz domains in ℝⁿ or ℂⁿContemporary Mathematics, 2005
- The null space of the $arpartial $-Neumann operatorAnnales de l'institut Fourier, 2004
- The Bergman kernel on the intersection of two balls in $ℂ^2$Duke Mathematical Journal, 2003
- Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifoldsMemoirs of the American Mathematical Society, 2001
- Hilbert complexesJournal of Functional Analysis, 1992
- Subelliptic Estimates for the $\overline \partial$-Neumann Problem on Pseudoconvex DomainsAnnals of Mathematics, 1987
- Regularity of the Bergman projection on domains with transverse symmetriesMathematische Annalen, 1982
- L 2 cohomology of warped products and arithmetic groupsInventiones Mathematicae, 1982
- Harmonic Integrals on Strongly Pseudo-Convex Manifolds, IAnnals of Mathematics, 1963
- Some Integration Problems in Almost-Complex and Complex ManifoldsAnnals of Mathematics, 1963