A kernel approach to the local solvability of the tangential Cauchy Riemann equations

Boggess, A.; Shaw, M.-C.

doi:10.1090/S0002-9947-1985-0784007-7

A kernel approach to the local solvability of the tangential Cauchy Riemann equations
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by A. Boggess and M.-C. Shaw PDF

Trans. Amer. Math. Soc. 289 (1985), 643-658 Request permission

Abstract:

An integral kernel approach is given for the proof of the theorem of Andreotti and Hill which states that the $Y(q)$ condition of Kohn is a sufficient condition for local solvability of the tangential Cauchy Riemann equations on a real hypersurface in ${{\mathbf {C}}^n}$. In addition, we provide an integral kernel approach to nonsolvability for a certain class of real hypersurfaces in the case when $Y(q)$ is not satisfied.

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