Geodesic
On the Hilbert Transform in Bergman Space
Matematičeskie zametki, Tome 70 (2001) no. 1, pp. 68-78.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we describe the image of the Hilbert transform operator for Bergman space. 
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R. S. Yulmukhametov; V. V. Napalkov. On the Hilbert Transform in Bergman Space. Matematičeskie zametki, Tome 70 (2001) no. 1, pp. 68-78. http://geodesic.mathdoc.fr/item/MZM_2001_70_1_a8/

[1] Derzhavets B. A., “Prostranstva funktsii, analiticheskikh v vypuklykh oblastyakh $\mathbb C^n$ i imeyuschikh zadannoe povedenie vblizi granitsy”, Dokl. AN SSSR, 276:6 (1984), 1297–1300 | MR | Zbl

[2] Lyubarskii Yu. I., “Teorema Vinera–Peli dlya vypuklykh mnozhestv”, Izv. AN ArmSSR. Matem., 62:2 (1988), 162–172

[3] Lutsenko V. I., Yulmukhametov R. S., “Obobschenie teoremy Vinera–Peli na funktsionaly v prostranstvakh Smirnova”, Tr. MIAN, 200, Nauka, M., 1991, 245–254 | Zbl

[4] Napalkov V. V. (ml.), Yulmukhametov R. S., “O preobrazovanii Koshi funktsionalov na prostranstve Bergmana”, Matem. sb., 185:7 (1994), 77–86 | Zbl

[5] Köthe G., “Dualität in der Funktionentheorie”, J. Reine Angew. Math., 191:1/2 (1953), 30–49 | MR | Zbl

[6] Khermander L., Vvedenie v teoriyu funktsii neskolkikh kompleksnykh peremennykh, Mir, M., 1986

[7] Yulmukhametov R. S., “Prostranstvo analiticheskikh funktsii, imeyuschikh zadannyi rost vblizi granitsy”, Matem. zametki, 32:1 (1982), 41–57 | MR | Zbl

[8] Napalkov V. V., “Prostranstva analiticheskikh funktsii zadannogo rosta vblizi granitsy”, Izv. AN SSSR. Ser. matem., 51:2 (1987), 287–305 | MR | Zbl

[9] Epifanov O. V., “Dvoistvennost odnoi pary prostranstv analiticheskikh funktsii ogranichennogo rosta”, Dokl. AN SSSR, 319:6 (1991), 1297–1300 | Zbl

[10] Merenkov S. A., “On the Cauchy transform of the Bergman space”, Matematicheskaya fizika, analiz, geometriya, no. 4, Kharkov, 1999

[11] Calderon A. P., “Cauchy integrals on Lipschitz curves and related operators”, Proc. Mat. Acad. Sci. USA, 1977, 1324–1327 | DOI | MR | Zbl

[12] Coifman R. R., McIntosh A., Meyer Y., “L'intégrale de Cauchy définit un opératuer bourné sur $L^2$ pour les courbes Lipschitziennes”, Annals of Math., 116:2 (1982) | DOI | MR | Zbl

[13] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973

[14] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966

[15] Krushkal S. L., Kyunau R., Kvazikonformnye otobrazheniya – novye metody i prilozheniya, Nauka, Novosibirsk, 1984 | Zbl

[16] Gaier D., Lektsii po teorii approksimatsii v kompleksnoi oblasti, Mir, M., 1987