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Journal of Function Spaces and Applications
Volume 2012, Article ID 265092, 27 pages
http://dx.doi.org/10.1155/2012/265092
Research Article

Weighted πœ• -Integral Representations of 𝐢 𝟏 -Functions in 𝐢 𝑛

Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan, Armenia

Received 28 July 2011; Accepted 13 August 2011

Academic Editor: Richard Rochberg

Copyright © 2012 Arman H. Karapetyan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. M. Djrbashian, β€œOn the representability of certain classes of entire functions,” Doklady Akademii Nauk ArmSSR, vol. 7, pp. 193–197, 1947 (Russian). View at Google Scholar
  2. M. M. Djrbashian, β€œOn the problem of representability of analytic functions,” Soobshch.Inst.Matem.Mekh. Akademii Nauk ArmSSR, vol. 2, pp. 3–40, 1948 (Russian). View at Google Scholar
  3. M. M. Dzhrbashyan and A. O. Karapetyan, β€œIntegral representations and uniqueness theorems for entire functions of several variables,” Journal of Contemporary Mathematical Analysis, vol. 26, no. 1, pp. 1–17, 1991. View at Google Scholar Β· View at Zentralblatt MATH
  4. B. Berndtsson and M. Andersson, β€œHenkin-Ramirez formulas with weight factors,” Annales de l'Institut Fourier, vol. 32, no. 3, pp. 91–110, 1982. View at Google Scholar
  5. J. Boo, β€œOn canonical homotopy operators for ¯ in Fock type spaces in Rn,” Publicacions Matemàtiques, vol. 45, no. 1, pp. 223–233, 2001. View at Publisher Β· View at Google Scholar
  6. P. H. Charpentier, β€œFormules explicites pour les solutions minimales de l'équation ¯u=f dans la boule et dans le polydisque de Cn,” Annales de l'Institut Fourier, vol. 30, no. 4, pp. 121–154, 1980. View at Publisher Β· View at Google Scholar
  7. B. Berndtsson, β€œIntegral formulas for the ¯-equation and zeros of bounded holomorphic functions in the unit ball,” Mathematische Annalen, vol. 249, no. 2, pp. 163–176, 1980. View at Publisher Β· View at Google Scholar
  8. M. Andersson, β€œFormulas for the L2 solutions of the ¯-equation in the unit ball of Cn,” Mathematica Scandinavica, vol. 56, no. 1, pp. 43–69, 1985. View at Google Scholar
  9. G. M. Henkin, β€œSolutions with bounds for the equations of H. Lewy and Poincaré-Lelong. Construction of functions of Nevanlinna class with given zeros in a strongly pseudoconvex domain,” Doklady Akademii Nauk SSSR, vol. 224, no. 4, pp. 771–774, 1975 (Russian). View at Google Scholar
  10. H. Skoda, β€œValeurs au bord pour les solutions de l'opérateur d et caractérisation des zéros des fonctions de la classe de Nevanlinna,” Bulletin de la Société Mathématique de France, vol. 104, no. 3, pp. 225–299, 1976. View at Google Scholar
  11. Š. A. Dautov and G. M. Henkin, β€œZeros of holomorphic functions of finite order and weighted estimates for the solutions of the ¯-equation,” Matematicheskiĭ Sbornik, vol. 107, no. 2, pp. 371–384, 1978 (Russian). View at Google Scholar
  12. M. Andersson, J. Boo, and J. Ortega-Cerdà, β€œCanonical homotopy operators for the ¯ complex in strictly pseudoconvex domains,” Bulletin de la Société Mathématique de France, vol. 126, no. 2, pp. 245–271, 1998. View at Google Scholar
  13. M. Andersson and J. Boo, β€œApproximate formulas for canonical homotopy operators for the ¯ complex in strictly pseudoconvex domains,” Mathematica Scandinavica, vol. 87, no. 2, pp. 251–271, 2000. View at Google Scholar
  14. A. H. Karapetyan, β€œWeighted ¯-integral representations in matrix domains,” Complex Variables and Elliptic Equations, vol. 53, no. 12, pp. 1131–1168, 2008. View at Publisher Β· View at Google Scholar
  15. M. M. Dzhrbashyan, β€œWeighted integral representations of analytic and smooth functions in the unit disk and in the complex plane,” Journal of Contemporary Mathematical Analysis, vol. 28, pp. 1–27, 1993. View at Google Scholar
  16. A. I. Petrosyan, β€œWeighted integral representations of functions in the polydisk and in the space Cn,” Journal of Contemporary Mathematical Analysis, vol. 31, no. 1, pp. 38–50, 1996. View at Google Scholar
  17. W. Rudin, Function Theory in the Unit Ball of Cn, Classics in Mathematics, Springer, Berlin, Germany, 1980.
  18. G. M. Henkin and J. Leiterer, Theory of Functions on Complex Manifolds, Springer, Basel, Switzerland, 1984.
  19. B. V. Shabat, Introduction to Complex Analysis, vol. 2, Nauka, Moscow, Russia, 1985.