Some applications of a new integral formula for $∂̅_{b}$

Volume 70 / 1998

Moulay Barkatou Annales Polonici Mathematici 70 (1998), 1-24 DOI: 10.4064/ap-70-1-1-24


Let M be a smooth q-concave CR submanifold of codimension k in $ℂ^n$. We solve locally the $∂̅_{b}$-equation on M for (0,r)-forms, 0 ≤ r ≤ q-1 or n-k-q+1 ≤ r ≤ n-k, with sharp interior estimates in Hölder spaces. We prove the optimal regularity of the $∂̅_{b}$-operator on (0,q)-forms in the same spaces. We also obtain $L^p$ estimates at top degree. We get a jump theorem for (0,r)-forms (r ≤ q-2 or r ≥ n-k-q+1) which are CR on a smooth hypersurface of M. We prove some generalizations of the Hartogs-Bochner-Henkin extension theorem on 1-concave CR manifolds.


  • Moulay Barkatou

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