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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Pointwise estimates for the relative fundamental solution of $ \overline\partial\sb b$


Author: Michael Christ
Journal: Proc. Amer. Math. Soc. 104 (1988), 787-792
MSC: Primary 35N15; Secondary 32F20, 32F30
DOI: https://doi.org/10.1090/S0002-9939-1988-0929407-5
MathSciNet review: 929407
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Abstract: Consider a compact pseudoconvex CR manifold of dimension 3 and finite type, on which the operator $ {\bar \partial _b}$ has closed range in $ {L^2}$. The relative fundamental solution of $ {\bar \partial _b}$ is the distribution-kernel for that operator which inverts $ {\bar \partial _b}$ modulo its kernel and cokernel. We derive pointwise bounds on this fundamental solution and its derivatives.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0929407-5
Article copyright: © Copyright 1988 American Mathematical Society