Geodesic
Banach cohomology of piecewise strictly pseudoconvex domains
Sbornik. Mathematics, Tome 17 (1972) no. 2, pp. 237-256 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove the directness and exactness of the Dolbeault Banach complex for a strictly pseudoconvex domain whose boundary consists of a finite series of smooth pieces which intersect in general position. Bibliography: 5 titles. 
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     author = {P. L. Polyakov},
     title = {Banach cohomology of piecewise strictly pseudoconvex domains},
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P. L. Polyakov. Banach cohomology of piecewise strictly pseudoconvex domains. Sbornik. Mathematics, Tome 17 (1972) no. 2, pp. 237-256. http://geodesic.mathdoc.fr/item/SM_1972_17_2_a5/

[1] G. M. Xenkin, “Integralnoe predstavlenie funktsii v strogo psevdovypuklykh oblastyakh i prilozheniya k $\overline\partial$-zadache”, Matem. sb., 82(124) (1970), 300–308

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

[3] I. Lieb, “Die Cauchy–Riemannschen Differentialgleichungen auf streng pseudokonvexen Gebieten”, Math. Ann., 190:1 (1970), 6–44 | DOI | MR | Zbl

[4] P. L. Polyakov, “Formula Koshi–Veilya dlya differentsialnykh form”, Matem. sb., 85(127) (1971), 388–402 | MR | Zbl

[5] A. Weil, “Sur les theoremes de de Rham”, Comm. Math. Helv., 26:2 (1952), 119–145 | DOI | MR | Zbl