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Inner functions and boundary values in \(H^\infty(\Omega)\) and \(A(\Omega)\) in smoothly bounded pseudoconvex domains. (English) Zbl 0526.32017


MSC:

32T99 Pseudoconvex domains
32E35 Global boundary behavior of holomorphic functions of several complex variables
32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
32A10 Holomorphic functions of several complex variables
32E30 Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs
32A38 Algebras of holomorphic functions of several complex variables

Citations:

Zbl 0508.32005
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References:

[1] Aleksandrov, A.B.: Existence of inner functions in the ball. Mat. Sb.117, 147-163 (1982) [Russian] · Zbl 0503.32001
[2] Aleksandrov, A.B.: Private communication. October 1982
[3] Beatrous, F. Jr.: H?lder estimates for the \(\bar \partial \) equation with a support condition. Pacific J. Math.90, 249-257 (1980) · Zbl 0453.32006
[4] Cole, B., Range, R.M.:A-measures on complex manifolds and some applications. J. Functional Analysis11, 393-400 (1972) · Zbl 0245.32008 · doi:10.1016/0022-1236(72)90061-4
[5] Fornaess, J.E.: Embedding strictly pseudoconvex domains in convex domains. Amer. J. Math.98, 529-569 (1976) · Zbl 0334.32020 · doi:10.2307/2373900
[6] Hakim, M., Sibony, N.: Fonctions holomorphes bornees sur la boule unite de ? n . Invent. Math.67, 213-222 (1982) · Zbl 0491.32014 · doi:10.1007/BF01393814
[7] Henkin, G.M.: Continuation of bounded holomorphic functions from submanifolds in general position to strictly pseudoconvex sets. Math. USSR-Izv.6, 536-563 (1972) · Zbl 0255.32008 · doi:10.1070/IM1972v006n03ABEH001889
[8] Krantz, S.G.: Function theory of several complex variables. New York: Wiley 1982 · Zbl 0471.32008
[9] L?w, E.: A construction of inner functions on the unit ball in ? p . Invent. Math.67, 223-229 (1982) · Zbl 0528.32006 · doi:10.1007/BF01393815
[10] Rudin, W.: Function theory in the unit ball of ? n . New York: Springer 1980 · Zbl 0495.32001
[11] Rudin, W.: Innrer functions in the unit ball of ? n . Preprint (1982)
[12] Sibony, N.: Valeurs au bord de fonctions holomorphes et ensembles polynomialement convexes. Lecture Notes in Math.578, pp. 300-313. Berlin-Heidelberg-New York: Springer 1977 · Zbl 0382.32004
[13] Stein, E.M.: Boundary behaviour of holomorphic functions of several complex variables. Princeton: Princeton University Press 1972 · Zbl 0242.32005
[14] Stens?nes Henriksen, B.: A peak set of Hausdorff dimension 2n?1 for the algebraA(D) in the boundary of a domainD withC ?-boundary in ? n . Math. Ann.259, 271-277 (1982) · Zbl 0483.32011 · doi:10.1007/BF01457313
[15] Stout, E.L., Duchamp, Th.: Maximum modulus sets. Ann. Inst. Fourier (Grenoble)31.3, 37-69 (1981) · Zbl 0439.32007
[16] Stout, E.L.: The dimension of peak-interpolation sets. Univ. of Washington, preprint 1982 · Zbl 0502.32012
[17] Tomaszewski, B.: The Schwarz lemma for inner functions in the unit ball in ? n . Univ. of Wisconsin, preprint 1982 · Zbl 0501.46021
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