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Mat. Sb. (N.S.), 1978, Volume 107(149), Number 2(10), Pages 163–174 (Mi msb2632)  

This article is cited in 12 scientific papers (total in 12 papers)

Zeros of holomorphic functions of finite order and weighted estimates for solutions of the $\bar\partial$-equation

Sh. A. Dautov, G. M. Henkin

Abstract: A characterization is given for the zero-sets of functions holomorphic in a strictly pseudoconvex manifold and having finite order of growth at the boundary of the manifold. The characterization is obtained by means of explicit formulas for solutions of the equation $\bar\partial u=f$ on a strictly convex domain in $\mathbf C^n$, valid for right sides $f$ having finite order of growth at the boundary of the domain.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1979, 35:4, 449–459

Bibliographic databases:

UDC: 517.55
MSC: Primary 32F15; Secondary 35N15
Received: 19.12.1977

Citation: Sh. A. Dautov, G. M. Henkin, “Zeros of holomorphic functions of finite order and weighted estimates for solutions of the $\bar\partial$-equation”, Mat. Sb. (N.S.), 107(149):2(10) (1978), 163–174; Math. USSR-Sb., 35:4 (1979), 449–459

Citation in format AMSBIB
\by Sh.~A.~Dautov, G.~M.~Henkin
\paper Zeros of holomorphic functions of finite order and weighted estimates for solutions of the $\bar\partial$-equation
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 107(149)
\issue 2(10)
\pages 163--174
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 4
\pages 449--459

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    This publication is cited in the following articles:
    1. Andersson M., “Solution Formulas for the Alpha-Alpha-Bar-Equation and Weighted Nevanlinna Classes in the Polydisk”, Bull. Sci. Math., 109:2 (1985), 135–154  mathscinet  zmath  isi
    2. Joaquín M. Ortega, Joan Fàbrega, “Extension ofA t-jets from holomorphic submanifolds”, Math Z, 212:1 (1993), 637  crossref  mathscinet  zmath  isi
    3. Li H., Luecking D., “Bmo on Strongly Pseudoconvex Domains - Hankel-Operators, Duality and Partial-Derivative-Estimates”, Trans. Am. Math. Soc., 346:2 (1994), 661–691  crossref  mathscinet  zmath  isi
    4. Elisabetta Barletta, Carla Parrini, “Bounded solutions for 119-01119-01119-01-problem in pseudo-Siegel domains”, Annali di Matematica, 168:1 (1995), 119  crossref  mathscinet  zmath  isi
    5. Joaquim Bruna, Xavier Massaneda, “Zero sets of holomorphic functions in the unit ball with slow growth”, J Anal Math, 66:1 (1995), 217  crossref  mathscinet  zmath  isi
    6. Andersson M., Carlsson H., “Formulas for Approximate Solutions of the Partial Derivative Partial Derivative-Equation in a Strictly Pseudoconvex Domain”, Rev. Mat. Iberoam., 11:1 (1995), 67–101  crossref  mathscinet  zmath  isi
    7. B HENNE, “Classes de Nevanlinna dans certains domaines strictement pseudoconvexes non lisses”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 326:4 (1998), 437  crossref
    8. Andersson M., “Integral Representation with Weights I”, Math. Ann., 326:1 (2003), 1–18  crossref  mathscinet  zmath  isi
    9. “LpESTIMATES WITH WEIGHTS FOR THE (equation omitted)-EQUATION ON REAL ELLIPSOIDS IN Cn”, Communications of the Korean Mathematical Society, 18:2 (2003), 263  crossref
    10. Ahn H., “Weighted l-P Estimates for the Partial Derivative-Equation on Convex Domains of Finite Type”, Publ. Mat., 48:1 (2004), 139–157  mathscinet  zmath  isi
    11. B. N. Khabibullin, A. P. Rozit, “On the Distribution of Zero Sets of Holomorphic Functions”, Funct. Anal. Appl., 52:1 (2018), 21–34  mathnet  crossref  crossref  isi  elib
    12. B. N. Khabibullin, Z. F. Abdullina, A. P. Rozit, “Teorema edinstvennosti i subgarmonicheskie testovye funktsii”, Algebra i analiz, 30:2 (2018), 318–334  mathnet  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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