Sobolev estimates for the local extension of ∂̄_{𝑏}-closed (0,1)-forms on real hypersurfaces in ℂⁿ with two positive eigenvalues

Cho, Sanghyun

doi:10.1090/S0002-9939-2011-10828-1

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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Proc. Amer. Math. Soc. 139 (2011), 4053-4062 Request permission

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.

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