التفاصيل البيبلوغرافية
| العنوان: |
Hartogs-Bochner extension theorem for L²loc-functions on unbounded domains. |
| المؤلفون: |
Khidr, Shaban, Sambou, Salomon |
| المصدر: |
ScienceAsia; 2024, Vol. 50 Issue 5, p1-4, 4p |
| مصطلحات موضوعية: |
COMPLEX manifolds, VANISHING theorems |
| مستخلص: |
We prove an L²loc-Hartogs-Bochner type extension theorem for unbounded domain D in a complex manifold X of complex dimension n ≥ 2. More precisely, we show that if Φ is a paracompactifying family of closed subsets of X not containing X, then the ...-cohomology group of (0, 1)-currents of class ... on X with supports in Φ is isomorphic to the ...-cohomology group of (0, 1)-forms with L²loc(X)-coefficients and with supports in Φ. Moreover, we prove that a sufficient condition for CR L²loc-functions, defined on the boundary ∂ D of D, being extended holomorphically to D is that the ...-cohomology groups must vanish. Similar results are given in the ... and Lp-categories. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
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