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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The $ \bar \partial $-Neumann solution to the inhomogeneous Cauchy-Riemann equation in the ball in $ {\bf C}\sp{n}$


Authors: F. Reese Harvey and John C. Polking
Journal: Trans. Amer. Math. Soc. 281 (1984), 587-613
MSC: Primary 32A25; Secondary 35N15
DOI: https://doi.org/10.1090/S0002-9947-1984-0722764-5
MathSciNet review: 722764
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Abstract: Let $ \vartheta $ denote the formal adjoint of the Cauchy-Riemann operator $ \overline \partial $ on $ {{\mathbf{C}}^n}$, and let $ N$ denote the Kohn-Neumann operator on the unit ball in $ {{\mathbf{C}}^n}$. The operator $ \vartheta \; \circ \;N$ provides a natural fundamental solution for $ \overline \partial f = g$ on the ball. It is our purpose to present the kernel $ P$ for this operator $ \vartheta \; \circ \;N$ explicitly--the coefficients are exhibited as rational functions.


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DOI: https://doi.org/10.1090/S0002-9947-1984-0722764-5
Article copyright: © Copyright 1984 American Mathematical Society