Geodesic
Integral representation of functions in strictly pseudoconvex domains and applications to the $\overline\partial$-problem
Sbornik. Mathematics, Tome 11 (1970) no. 2, pp. 273-281 
G. M. Henkin. Integral representation of functions in strictly pseudoconvex domains and applications to the $\overline\partial$-problem. Sbornik. Mathematics, Tome 11 (1970) no. 2, pp. 273-281. http://geodesic.mathdoc.fr/item/SM_1970_11_2_a10/
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     title = {Integral representation of functions in strictly pseudoconvex domains and applications to the $\overline\partial$-problem},
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     volume = {11},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1970_11_2_a10/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The integral representation obtained for smooth functions defined in strictly pseudoconvex domains in $n$-dimensional complex space can be considered as the “natural” extension of the well-known Cauchy–Green formula. Using this representation we succeed in obtaining a formula and uniform bound for solutions of the $\overline\partial$-problem in strictly pseudoconvex domains. Bibliography: 11 titles.

[1] R. Ganning, X. Rossi, Analiticheskie funktsii mnogikh kompleksnykh peremennykh, Mir, Moskva, 1969 | MR

[2] C. B. Morrey, “The analytic embedding of abstract real-analytic manifolds”, Ann. Math., 68 (1958), 150–201 | DOI | MR

[3] J. J. Kohn, “Harmonic integrals on strongly pseudoconvex manifolds”, Ann. Math., 78 (1963), 112–148 ; 79 (1964), 450–472 | DOI | MR | Zbl | DOI | MR | Zbl

[4] L. Hörmander, “$L^2$ estimates and existence theorems for the $\overline\partial$-operator”, Acta Math., 113:1–2 (1965), 89–152 | DOI | MR | Zbl

[5] K. Oka, “Sur les fonctions analytiqnes des plusieors variables complexes”, J. Sci. Hirosima Univ., 6 (1936), 245–255 ; 7 (1937), 115–130 ; 9 (1939), 7–19 | MR | Zbl | Zbl | MR | Zbl

[6] K. Oka, “Domaines finis sans point critique interieur”, Japan. J. Math., 23 (1953), 97–155 | MR | Zbl

[7] S. Bochner, “Analytic and meromorphic continuation by means of Green's formula”, Ann. Math., 44 (1943), 652–673 | DOI | MR | Zbl

[8] G. M. Khenkin, “Integralnoe predstavlenie funktsii, golomorfnykh v strogo psevdovypuklykh oblastyakh, i nekotorye prilozheniya”, Matem. sb., 78(120) (1969), 611–632 | Zbl

[9] Zh. Lere, Differentsialnoe i integralnoe ischisleniya na kompleksnom analiticheskom mnogoobrazii, IL, Moskva, 1961

[10] I. Lieb, “Ein Approximationssatz auf streng pseudokonvexen Gebieten”, Math. Ann., 184:1 (1969), 56–60 | DOI | MR | Zbl

[11] H. Grauert, I. Lieb, Das Ramirezsche Integral und die Lösung der Gleichung $\overline\partial f=\alpha$ im Bereich der beschränkten Formen in Rigc University Studies Houston (to appear)