The ∂̄ Neumann problem is probably the most important and natural example of a non-elliptic boundary value problem, arising as it does from the Cauchy-Riemann equations. It has been known for some time how to prove solvability and regularity by the use of L2 methods. In this monograph the authors apply recent methods involving the Heisenberg group to obtain parametricies and to give sharp estimates in various function spaces, leading to a better understanding of the ∂̄ Neumann problem. The authors have added substantial background material to make the monograph more accessible to students.
Originally published in 1977.
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Table of Contents:
- Frontmatter, pg. i
- Preface, pg. iii
- Table of Contents, pg. v
- Introduction, pg. 1
- Part I. Analysis on the Heisenberg group, pg. 10
- Part II. Parametrix for the ∂̄ -Neumann problem, pg. 44
- Part III. The Estimates, pg. 130
- Principal notations, pg. 190
- References, pg. 192