Skoda, Henri Valeurs au bord pour les solutions de l’opérateur \(d^n\), et caractérisation des zéros des fonctions de la classe de Nevanlinna. (French) Zbl 0351.31007 Bull. Soc. Math. Fr. 104, 225-299 (1976). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 59 Documents MSC: 31B20 Boundary value and inverse problems for harmonic functions in higher dimensions 32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.) × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] CARLESON (L.) . - Interpolations by bounded analytic functions and the corona problem , Ann. of Math., t. 76, 1962 , p. 547-559. MR 25 #5186 | Zbl 0112.29702 · Zbl 0112.29702 · doi:10.2307/1970375 [2] CARLESON (L.) . - The corona theorem , Proocedings of the 15th Scandinavian Congress [ 1968 , Oslo] , p. 121-132. - Berlin, Heidelberg, New York, Springer-Verlag, 1970 (Lecture Notes in Mathematics, 118). Zbl 0195.42104 · Zbl 0195.42104 [3] CHEE PAK SONG . - The Blaschke condition for bounded holomorphic function , Trans. Amer. math. Soc., t. 148, 1970 , p. 248-263. MR 41 #7147 | Zbl 0196.09503 · Zbl 0196.09503 · doi:10.2307/1995050 [4] FOLLAND (G. B.) and KOHN (J. J.) . - The Neumann problem for the Cauchy-Riemann complex . - Princeton, Princeton University Press 1972 , (Annals of Mathematics Studies, 75). MR 57 #1573 | Zbl 0247.35093 · Zbl 0247.35093 [5] FOLLAND (G. B.) and STEIN (E. M.) . - Parametrices and estimates for the \partial b complex on strongly pseudoconvex boundaries , Bull. Amer. math. Soc., t. 80, 1974 , p. 253-258. Article | MR 49 #9438 | Zbl 0294.35059 · Zbl 0294.35059 · doi:10.1090/S0002-9904-1974-13449-X [6] FOLLAND (G. B.) and STEIN (E. M.) . - Estimates for the \partial b complex and analysis on the Heisenberg group , Comm. pure and appl. Math., t. 27, 1974 , p. 429-522. MR 51 #3719 | Zbl 0293.35012 · Zbl 0293.35012 · doi:10.1002/cpa.3160270403 [7] GRAUERT (H.) und LIEB (I.) . - Das Ramirezsche Integral und die Lösung der Gleichung \partial f = \alpha im Bereich der beschränkten Formen , Complex analysis. Proceedings of the conference at Rice University [ 1969 , Houston] , p. 29-50. - Houston, William Marsh Rice University, 1971 (Rice University Studies, 56, n^\circ 2). Zbl 0217.39202 · Zbl 0217.39202 [8] GRUMAN (L.) . - The zeros of holomorphic functions in strictly pseudoconvex domains , Trans. Amer. math. Soc. (à paraître). Zbl 0308.32014 · Zbl 0308.32014 · doi:10.2307/1997172 [9] HENKIN (G. M.) . - Integral representations of functions holomorphic in strictly pseudoconvex domains, and some applications , Math. USSR-Sbornik, t. 7, 1969 , p. 597-616 ; [in Russian] Mat. Sbornik, t. 78 (120), 1969 , p. 611-632. Zbl 0208.35102 · Zbl 0208.35102 · doi:10.1070/SM1969v007n04ABEH001105 [10] HENKIN (G. M.) . - Integral representations of functions in strictly pseudoconvex domains and application to the \partial -problem , Math. USSR-Sbornik, t. 11, 1970 , p. 273-282 ; [in Russian] Mat. Sbornik, t. 82 (124), 1970 , p. 300-308. Zbl 0216.10402 · Zbl 0216.10402 · doi:10.1070/SM1970v011n02ABEH002069 [11] HENKIN (G. M.) . - Rešenija s ocenkami uravnenij G. Levi i Puankare-Lelona... , Doklady Akad. Nauk. SSSR, t. 224, 1975 , p. 771-774. MR 57 #6511 [12] HOFFMAN (K.) . - Banach spaces of analytic functions . - Englewood Cliffs, Prentice-Hall, 1962 (Prentice-Hall Series in moder Analysis). MR 24 #A2844 | Zbl 0117.34001 · Zbl 0117.34001 [13] HÖRMANDER (L.) . - Lp estimates for (pluri-) subharmonic functions , Math. Scand., t. 20, 1967 , p. 65-78. Zbl 0156.12201 · Zbl 0156.12201 [14] HÖRMANDER (L.) . - Generators for some rings of analytic functions , Bull. Amer. math. Soc., t. 73, 1967 , p. 943-949. Article | MR 37 #1977 | Zbl 0172.41701 · Zbl 0172.41701 · doi:10.1090/S0002-9904-1967-11860-3 [15] KERZMAN (N.) . - Hölder and Lp estimates for the solutions of \partial u = f in strongly pseudoconvex domains , Comm. pure and appl. Math., t. 24, 1971 , p. 301-379. MR 43 #7658 | Zbl 0205.38702 · Zbl 0205.38702 · doi:10.1002/cpa.3160240303 [16] KERZMAN (N.) and NAGEL (A.) . - On finitely generated ideals in certain function algebras , J. Funct. Anal., t. 7, 1971 , p. 212-215. MR 43 #929 | Zbl 0211.43902 · Zbl 0211.43902 · doi:10.1016/0022-1236(71)90053-X [17] KOPPELMAN (W.) . - The Cauchy Integral for differential forms , Bull. Amer. math. Soc., t. 73, 1967 , p. 554-556. Article | MR 35 #6862 | Zbl 0186.13803 · Zbl 0186.13803 · doi:10.1090/S0002-9904-1967-11744-0 [18] LAVILLE (G.) . - Résolution du \partial avec croissance dans les ouverts pseudo-convexes étoilés de Cn , C. R. Acad. Sc. Paris, t. 274, 1972 , série A, p. 554-556. MR 45 #3760 | Zbl 0239.32014 · Zbl 0239.32014 [19] LAVILLE (G.) . - Diviseurs et classes de Nevanlinna , Thèse 3e cycle, Univ. P.-et-M.-Curie [Paris-VI], 1975 . MR 52 #14358 · Zbl 0326.32010 [20] LELONG (P.) . - Intégration sur un ensemble analytique complexe , Bull. Soc. math. France, t. 85, 1957 , p. 239-262. Numdam | MR 20 #2465 | Zbl 0079.30901 · Zbl 0079.30901 [21] LELONG (P.) . - Fonctionnelles analytiques et fonctions entières (n variables) . - Montréal, les Presses de l’Université de Montréal, 1968 (Séminaire de Mathématiques supérieures, Été 1967 , 28). Zbl 0194.38801 · Zbl 0194.38801 [22] LELONG (P.) . - Fonctions plurisousharmoniques et formes différentielles positives . - Paris, Londres, New York, Gordon and Breach, Dunod, 1968 (Cours et Documents de Mathématiques et de Physique). MR 39 #4436 | Zbl 0195.11603 · Zbl 0195.11603 [23] LIEB (I.) . - Die Cauchy Riemannschen Differentialgleichungen auf streng pseudokonvex Gebieten , Math. Annalen, t. 190, 1970 , p. 6-44. MR 44 #468 | Zbl 0199.42702 · Zbl 0199.42702 · doi:10.1007/BF01349966 [24] MALLIAVIN (P.) . - Fonctions de Green d’un ouvert strictement pseudoconvexe et de classe de Nevanlinna , C. R. Acad. Sc. Paris, t. 278, 1974 , série A, p. 141-144. MR 49 #10919 | Zbl 0279.32005 · Zbl 0279.32005 [25] MUELLER (G.) . - Functions of finite order in the ball , Thesis, University of Notre-Dame, 1971 . [26] OVRELID (N.) . - Integral representation formulas and Lp estimates for the \partial -equation , Math. Scand., t. 29, 1971 , p. 137-160. MR 48 #2425 | Zbl 0227.35069 · Zbl 0227.35069 [27] OVRELID (N.) . - Integral representation formulas for differential formes and solutions of the \partial -equation , Colloque international du C.N.R.S., n^\circ 208 : Fonctions analytiques de plusieurs variables et analyse complexe . - Paris, Gauthier-Villars, 1974 (Agora Mathematica). Zbl 0304.32006 · Zbl 0304.32006 [28] RAMIREZ de ARELLANO (E.) . - Ein Divisionsproblem und Randintegraldarstellungen in der komplexen Analysis , Math. Annalen, t. 184, 1970 , p. 172-187. MR 42 #4767 | Zbl 0189.09702 · Zbl 0189.09702 · doi:10.1007/BF01351561 [29] RANGE (M.) and SIU (Y. T.) . - Uniform estimates for the \partial -equation on domains with piecewise smooth strictly pseudoconvex boundaries , Preprint, Yale University, 1972 . [30] ROMANOV (A. V.) . - Formula i ocenki dlja rešenij kasatel’nogo uravnenija Koŝi-Rimana , Doklady Akad. Nauk SSSR, t. 220, 1975 , p. 532-535. MR 52 #6037 | Zbl 0324.35070 · Zbl 0324.35070 [31] ROOS (G.) . - L’intégrale de Cauchy dans Cn , Preprint, Université de Paris-VII, 1970 - 1971 . [32] ROOS (G.) . - Formules intégrales pour les formes différentielles sur Cn , I, Annali della Scuola Normale di Pisa, t. 26, 1972 , p. 171-179. Numdam | MR 51 #3495 | Zbl 0243.32004 · Zbl 0243.32004 [33] SERRE (J.-P.) . - Un théorème de dualité , Comment. math. Helvet., t. 29, 1955 , p. 9-26. MR 16,736d | Zbl 0067.16101 · Zbl 0067.16101 · doi:10.1007/BF02564268 [34] SIU (Y. T.) and TRAUTMANN (G.) . - Gap-sheaves and extension of coherent analytic subsheaves . - Berlin, Heidelberg, New York, Springer-Verlag, 1971 (Lecture Notes in Mathematics, 172). MR 44 #4240 | Zbl 0208.10403 · Zbl 0208.10403 [35] SKODA (H.) . - Sous-ensembles analytiques d’ordre fini ou infini dans Cn , Bull. Soc. math. France, t. 100, 1972 , p. 353-408. Numdam | MR 50 #5004 | Zbl 0246.32009 · Zbl 0246.32009 [36] SKODA (H.) . - Valeurs au bord pour les solutions de l’opérateur d\(^{\prime\prime}\) dans les ouverts strictement pseudo-convexes , C.R. Acad. Sc. Paris, t. 280, 1975 , série A, p. 633-636. MR 51 #8466 | Zbl 0302.32021 · Zbl 0302.32021 [37] SKODA (H.) . - Zéros des fonctions de la classe de Nevanlinna dans les ouverts strictement pseudo-convexes , C.R. Acad. Sc. Paris, t. 280, 1975 , série A, p. 1677-1680. MR 52 #6020 | Zbl 0304.32001 · Zbl 0304.32001 [38] STEIN (E. M.) . - Boundary behavior of holomorphic functions of several complex variables . - Princeton, Princeton University Press, 1972 (Mathematical Notes). MR 57 #12890 | Zbl 0242.32005 · Zbl 0242.32005 [39] STOUT (E. L.) . - The second cousin problem with bounded data , Pacific J. Math., t. 26, 1968 , p. 379-387. Article | MR 38 #3467 | Zbl 0183.35201 · Zbl 0183.35201 · doi:10.2140/pjm.1968.26.379 [40] STOUT (E. L.) . - On the multiplicative cousin problem with bounded data , Annali della Scuola Normale Superiore di Pisa (à paraître). Numdam | Zbl 0261.32008 · Zbl 0261.32008 [41] HARVEY (R.) . - Summer Institut on several complex variables , at Williamstown, August 1975 , edited by the American Mathematical Society. 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. 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