Some applications of a new integral formula for ∂ ̅ b

Moulay-Youssef Barkatou

Annales Polonici Mathematici (1998)

  • Volume: 70, Issue: 1, page 1-24
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Moulay-Youssef Barkatou. "Some applications of a new integral formula for $∂̅_{b}$." Annales Polonici Mathematici 70.1 (1998): 1-24. <http://eudml.org/doc/262710>.

@article{Moulay1998,
abstract = {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.},
author = {Moulay-Youssef Barkatou},
journal = {Annales Polonici Mathematici},
keywords = {CR manifold; tangential Cauchy-Riemann equations; q-convexity; -convexity; -concavity; 1-concave CR manifolds; integral formulas; Hartogs extension theorem},
language = {eng},
number = {1},
pages = {1-24},
title = {Some applications of a new integral formula for $∂̅_\{b\}$},
url = {http://eudml.org/doc/262710},
volume = {70},
year = {1998},
}

TY - JOUR
AU - Moulay-Youssef Barkatou
TI - Some applications of a new integral formula for $∂̅_{b}$
JO - Annales Polonici Mathematici
PY - 1998
VL - 70
IS - 1
SP - 1
EP - 24
AB - 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.
LA - eng
KW - CR manifold; tangential Cauchy-Riemann equations; q-convexity; -convexity; -concavity; 1-concave CR manifolds; integral formulas; Hartogs extension theorem
UR - http://eudml.org/doc/262710
ER -

References

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