The L 2 ∂ ¯ -Cauchy problem on weakly q -pseudoconvex domains in Stein manifolds

Sayed Saber

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 3, page 739-745
  • ISSN: 0011-4642

Abstract

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Let X be a Stein manifold of complex dimension n ≥ 2 and Ω ⋐ X be a relatively compact domain with C 2 smooth boundary in X . Assume that Ω is a weakly q -pseudoconvex domain in X . The purpose of this paper is to establish sufficient conditions for the closed range of ∂ ¯ on Ω . Moreover, we study the ∂ ¯ -problem on Ω . Specifically, we use the modified weight function method to study the weighted ∂ ¯ -problem with exact support in Ω . Our method relies on the L 2 -estimates by Hörmander (1965) and by Kohn (1973).

How to cite

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Saber, Sayed. "The $L^2$$\bar{\partial }$-Cauchy problem on weakly $q$-pseudoconvex domains in Stein manifolds." Czechoslovak Mathematical Journal 65.3 (2015): 739-745. <http://eudml.org/doc/271800>.

@article{Saber2015,
abstract = {Let $X$ be a Stein manifold of complex dimension $n\ge 2$ and $\Omega \Subset X$ be a relatively compact domain with $C^2$ smooth boundary in $X$. Assume that $\Omega $ is a weakly $q$-pseudoconvex domain in $X$. The purpose of this paper is to establish sufficient conditions for the closed range of $\bar\{\partial \}$ on $\Omega $. Moreover, we study the $\bar\{\partial \}$-problem on $\Omega $. Specifically, we use the modified weight function method to study the weighted $\bar\{\partial \}$-problem with exact support in $\Omega $. Our method relies on the $L^2$-estimates by Hörmander (1965) and by Kohn (1973).},
author = {Saber, Sayed},
journal = {Czechoslovak Mathematical Journal},
keywords = {$\bar\{\partial \}$ operator; $\bar\{\partial \}$-Neumann operator; $q$-convex domain; Stein manifold},
language = {eng},
number = {3},
pages = {739-745},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The $L^2$$\bar\{\partial \}$-Cauchy problem on weakly $q$-pseudoconvex domains in Stein manifolds},
url = {http://eudml.org/doc/271800},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Saber, Sayed
TI - The $L^2$$\bar{\partial }$-Cauchy problem on weakly $q$-pseudoconvex domains in Stein manifolds
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 3
SP - 739
EP - 745
AB - Let $X$ be a Stein manifold of complex dimension $n\ge 2$ and $\Omega \Subset X$ be a relatively compact domain with $C^2$ smooth boundary in $X$. Assume that $\Omega $ is a weakly $q$-pseudoconvex domain in $X$. The purpose of this paper is to establish sufficient conditions for the closed range of $\bar{\partial }$ on $\Omega $. Moreover, we study the $\bar{\partial }$-problem on $\Omega $. Specifically, we use the modified weight function method to study the weighted $\bar{\partial }$-problem with exact support in $\Omega $. Our method relies on the $L^2$-estimates by Hörmander (1965) and by Kohn (1973).
LA - eng
KW - $\bar{\partial }$ operator; $\bar{\partial }$-Neumann operator; $q$-convex domain; Stein manifold
UR - http://eudml.org/doc/271800
ER -

References

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