Low, Erik Inner functions and boundary values in \(H^\infty(\Omega)\) and \(A(\Omega)\) in smoothly bounded pseudoconvex domains. (English) Zbl 0526.32017 Math. Z. 185, 191-210 (1984). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 13 Documents 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 Keywords:smoothly bounded pseudoconvex domains; inner functions; boundary values Citations:Zbl 0508.32005 PDFBibTeX XMLCite \textit{E. Low}, Math. Z. 185, 191--210 (1984; Zbl 0526.32017) Full Text: DOI EuDML 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.