## Sobolev estimates for the local extension of $\bar {\partial }_b$-closed $(0,1)$-forms on real hypersurfaces in $\mathbb C^n$ with two positive eigenvalues

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## Abstract:

Let $\mathcal M$ be a smooth real hypersurface in complex space of dimension $n\ge 3$, and assume that the Levi-form at $z_0$ on $\mathcal M$ has at least two positive eigenvalues. We estimate solutions of the local $\bar {\partial }$-closed extension problem near $z_0$ for $(0,1)$-forms in Sobolev spaces. Using this result, we estimate the local solution of tangential Cauchy-Riemann equations near $z_0$ for $(0,1)$-forms in Sobolev spaces.## References

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## Additional Information

**Sanghyun Cho**- Affiliation: Department of Mathematics, Sogang University, Seoul, 121-742, Republic of Korea
- Email: shcho@sogang.ac.kr
- Received by editor(s): July 22, 2010
- Received by editor(s) in revised form: October 5, 2010
- Published electronically: April 11, 2011
- Additional Notes: The author was partially supported by KRF-2005-070-C00007 and the Sogang University research fund.
- Communicated by: Mei-Chi Shaw
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**139**(2011), 4053-4062 - MSC (2010): Primary 32V25; Secondary 32W10
- DOI: https://doi.org/10.1090/S0002-9939-2011-10828-1
- MathSciNet review: 2823050