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Régularité hölderienne du ...b dans les hypersurfaces 1-convexes-concaves.

Moulay-Youssef Barkatou — 1996

Mathematische Zeitschrift

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

Moulay-Youssef Barkatou — 1998

Annales Polonici Mathematici

Let M be a smooth q-concave CR submanifold of codimension k in $ℂ^{n}$ . We solve locally the $\partial ̅_{b}$ -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 $\partial ̅_{b}$ -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...

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Régularité hölderienne du ...b dans les hypersurfaces 1-convexes-concaves.

Some applications of a new integral formula for ∂ ̅ b

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