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

Moulay-Youssef Barkatou

Annales Polonici Mathematici, Tome 69 (1998), p. 1-24 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 1998-01-01

Zbl 0927.32008

EUDML-ID : urn:eudml:doc:262710

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