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Non-Subelliptic estimates for the tangential Cauchy-Riemann system

H. Ahn·L. Baracco·G. Zampieri
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Abstract

We prove non-subelliptic estimates for the tangential Cauchy-Riemann system over a weakly "$q$-pseudoconvex" higher codimensional submanifold $M$ of $\C^n$. Let us point out that our hypotheses do not suffice to guarantee subelliptic estimates, in general. Even more: hypoellipticity of the tangential C-R system is not in question (as shows the example by Kohn in case of a Levi-flat hypersurface). However our estimates suffice for existence of smooth solutions to the inhomogeneous C-R equations in certain degree. The main ingredients in our proofs are the weighted $L^2$ estimates by Hörmander and Kohn and the tangential $\bar\partial$-Neumann operator by Kohn. As for the notion of $q$ pseudoconvexity we follow closely Zampieri. The main technical result is a version for "perturbed" $q$-pseudoconvex domains of a similar result by Ahn who generalizes in turn Chen-Shaw.

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H. Ahn, L. Baracco, G. Zampieri. 2005-05-16. Non-Subelliptic estimates for the tangential Cauchy-Riemann system. https://arxiv.org/abs/math/0505338

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