L p -estimates for solutions of ∂ ¯ -equation on strongly q -convex domains

Osama Abdelkader; Sh. Khidr

Mathematica Slovaca (2004)

  • Volume: 54, Issue: 4, page 337-348
  • ISSN: 0232-0525

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Abdelkader, Osama, and Khidr, Sh.. "$L^p$-estimates for solutions of $\overline{\partial }$-equation on strongly $q$-convex domains." Mathematica Slovaca 54.4 (2004): 337-348. <http://eudml.org/doc/32183>.

@article{Abdelkader2004,
author = {Abdelkader, Osama, Khidr, Sh.},
journal = {Mathematica Slovaca},
keywords = {-estimate; -equation; strongly -convex; smooth boundary; complex manifold},
language = {eng},
number = {4},
pages = {337-348},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {$L^p$-estimates for solutions of $\overline\{\partial \}$-equation on strongly $q$-convex domains},
url = {http://eudml.org/doc/32183},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Abdelkader, Osama
AU - Khidr, Sh.
TI - $L^p$-estimates for solutions of $\overline{\partial }$-equation on strongly $q$-convex domains
JO - Mathematica Slovaca
PY - 2004
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 54
IS - 4
SP - 337
EP - 348
LA - eng
KW - -estimate; -equation; strongly -convex; smooth boundary; complex manifold
UR - http://eudml.org/doc/32183
ER -

References

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  1. ABDELKADER O., L p -estimates for solution of δ -equation in strongly pseudo-convex domains, Tensor (N.S) 58 (1997), 128-136. (1997) Zbl1014.32026MR1697822
  2. ABDELKADER O., Un théorème ďannulation pour les fibrés endroites semi-positifs sur une variété Kählérienne faibement 1-complète, In: Complex Analysis-Fifth Romanian-Finish Seminar Part 2. Lecture Notes in Math. 1014, Springer-Verlag, New York, 1981, pp. 1-16. (1981) MR0738110
  3. ABDELKADER O.-KHIDR, SH., Solutions to ∂ ¯ -equations on strongly pseudo-convex domains with L p -estimates, Electron. J. Differential Equations 73 (2004), 1-9, http://ejde.math.txstate.edu, http://ejde.math.unt.edu, or ftp ejde.math.txstate.edu (login: ftp). MR2057660
  4. ABDELKADER O.-SABER S., On the vanishing theorem of Grauert-Riemeschneider, In: Proceeding of the International Conference of Mathematics (Trends and Developments) of the Egyptian Mathematical Society, Cairo, Egypt, 28-31 December (2002) (To appear in Egyptian Mathematical Society 2004). MR2084879
  5. ANDREOTTI A.-GRAUERT H., Theoreme de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France 90 (1962), 193-259. (1962) MR0150342
  6. HÖRMANDER L., An Introduction to Complex Analysis in Several Variables, Van Nostrand, Princeton, N.J., 1990. (1990) Zbl0685.32001MR1045639
  7. HÖRMANDER L., L 2 -estimates and existence theorems for the ∂ ¯ -operator, Acta Math. 113 (1965), 89-152. (1965) Zbl0158.11002MR0179443
  8. KOHN J. J.-ROSSI H., On the extension of holomorphic functions from the boundary of a complex manifold, Ann. of Math. 81 (1965), 451-472. (1965) MR0177135
  9. KERZMAN N., Hölder and L p -estimates for solutions of ∂ ¯ u = f in strongly pseudoconvex domains, Comm. Pure Appl. Math. 24 (1971), 301-380. (1971) Zbl0217.13202MR0281944
  10. LAN M., Hölder and L p -estimates for the ∂ ¯ -equation on non-smooth strictly q -convex domains, Manuscripta Math. 74 (1992), 177-193. (1992) Zbl0754.35092MR1147561
  11. OVRELID N., Integral representation formulas and L p -estimates for ∂ ¯ -equation, Math. Scand. 29 (1971), 137-160. (1971) MR0324073

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