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Uniform subelliptic estimates on scaled convex domains of finite type. (English) Zbl 0988.32021

The author shows that a gap in the proof of Proposition 3.1 of his earlier paper [Adv. Math. 109, No. 1, 108-139 (1994; Zbl 0816.32018)] can be repaired by using non-isotropic support functions of K. Diederich and J. E. Fornaess [Math. Z. 230, No. 1, 145-164 (1999; Zbl 1045.32016)].
Reviewer: J.Siciak (Kraków)

MSC:

32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
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[1] Joaquim Bruna, Philippe Charpentier, and Yves Dupain, Zero varieties for the Nevanlinna class in convex domains of finite type in \?\(^{n}\), Ann. of Math. (2) 147 (1998), no. 2, 391 – 415. · Zbl 0912.32001 · doi:10.2307/121013
[2] Joaquim Bruna, Alexander Nagel, and Stephen Wainger, Convex hypersurfaces and Fourier transforms, Ann. of Math. (2) 127 (1988), no. 2, 333 – 365. · Zbl 0666.42010 · doi:10.2307/2007057
[3] David Catlin, Subelliptic estimates for the \overline\partial -Neumann problem on pseudoconvex domains, Ann. of Math. (2) 126 (1987), no. 1, 131 – 191. · Zbl 0627.32013 · doi:10.2307/1971347
[4] A. Cumenge, Sharp estimates for \(\bar \partial \) on convex domains of finite type, Ark. Mat. 39 (2001), 1-25. · Zbl 1028.35115
[5] -, Zero sets of functions in the Nevanlinna class in convex domains of finite type (preprint).
[6] Klas Diederich and John Erik Fornæss, Support functions for convex domains of finite type, Math. Z. 230 (1999), no. 1, 145 – 164. · Zbl 1045.32016 · doi:10.1007/PL00004683
[7] John Erik Fornæss and Nessim Sibony, Construction of P.S.H. functions on weakly pseudoconvex domains, Duke Math. J. 58 (1989), no. 3, 633 – 655. · Zbl 0679.32017 · doi:10.1215/S0012-7094-89-05830-4
[8] S. G. Krantz and S.-Y. Li, Duality theorems for Hardy and Bergman spaces on convex domains of finite type in \?\(^{n}\), Ann. Inst. Fourier (Grenoble) 45 (1995), no. 5, 1305 – 1327 (English, with English and French summaries). · Zbl 0835.32004
[9] Jeffery D. McNeal, Estimates on the Bergman kernels of convex domains, Adv. Math. 109 (1994), no. 1, 108 – 139. · Zbl 0816.32018 · doi:10.1006/aima.1994.1082
[10] Jeffery D. McNeal, Convex domains of finite type, J. Funct. Anal. 108 (1992), no. 2, 361 – 373. · Zbl 0777.31007 · doi:10.1016/0022-1236(92)90029-I
[11] J. D. McNeal and E. M. Stein, The Szegő projection on convex domains, Math. Z. 224 (1997), no. 4, 519 – 553. · Zbl 0948.32004 · doi:10.1007/PL00004593
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