SOBOLEV ESTIMATES FOR THE LOCAL EXTENSION OF BOUNDARY HOLOMORPHIC FORMS ON REAL HYPERSURFACES IN ℂn

Title & Authors
SOBOLEV ESTIMATES FOR THE LOCAL EXTENSION OF BOUNDARY HOLOMORPHIC FORMS ON REAL HYPERSURFACES IN ℂn
Cho, Sanghyun;

Abstract
Let M be a smooth real hypersurface in complex space of dimension $\small{n}$, $\small{n{\geq}3}$, and assume that the Levi-form at $\small{z_0}$ on M has at least $\small{(q+1)}$-positive eigenvalues, $\small{1{\leq}q{\leq}n-2}$. We estimate solutions of the local $\small{\bar{\partial}}$-closed extension problem near $\small{z_0}$ for $\small{(p,q)}$-forms in Sobolev spaces. Using this result, we estimate the local solution of tangential Cauchy-Riemann equation near $\small{z_0}$ in Sobolev spaces.
Keywords
tangential Cauchy-Riemann equation;boundary holomorphic forms;
Language
English
Cited by
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