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Title

Some applications of a new integral formula for ∂̅b

Authors 1

Affiliations

  1. Département de Mathématiques Université de Poitiers 40 Avenue du Recteur Pineau 86022 Poitiers Cedex, France

Abstract

Let M be a smooth q-concave CR submanifold of codimension k in ℂn. 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 Lp 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.

Keywords

ENG
CR manifold, tangential Cauchy-Riemann equations, q-convexity

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Annales Polonici Mathematici
1998/70/1
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Pages:
1-24
Main language of publication
English
Received
1997-12-28
Accepted
1998-08-31
Published
1998
Exact and natural sciences