Geodesic
Solvability of the Dirichlet Problem with Boundary Functions from Weight Spaces
Matematičeskie zametki, Tome 76 (2004) no. 5, pp. 643-650 
H. M. Hayrapetyan. Solvability of the Dirichlet Problem with Boundary Functions from Weight Spaces. Matematičeskie zametki, Tome 76 (2004) no. 5, pp. 643-650. http://geodesic.mathdoc.fr/item/MZM_2004_76_5_a0/
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     author = {H. M. Hayrapetyan},
     title = {Solvability of the {Dirichlet} {Problem} with {Boundary} {Functions} from {Weight} {Spaces}},
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     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_5_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study the Dirichlet problem in the half-plane in weight spaces when the weight function has a unique singularity at the point at infinity.

[1] Khvedelidze B. V., “O razryvnoi zadache Rimana–Privalova dlya neskolkikh funktsii”, Soobschenie AN Gruz. SSR, 17:10 (1956), 865–872 | MR

[2] Rosenblum M., “Summability of Fourier series in $L_p(d\mu)$”, Trans. Amer. Math. Soc., 165 (1962), 326–342 | MR

[3] Tovmasyan N. E., “O suschestvovanii i edinstvennosti resheniya zadachi Dirikhle dlya uravneniya Laplasa v klasse funktsii, imeyuschikh osobennosti na granitse”, Sib. matem. zh., 2:2 (1961), 25–57

[4] Gokhberg I. Ts., Krupnik N. Ya., Vvedenie v teoriyu odnomernykh singulyarnykh integralnykh operatorov, Kishinëv, 1973

[5] Hunt R. A., Muckenhoupt B., Wheeden R. L., “Weighted norm inequalities for the conjugate functions and Hilbert transform”, Trans. Amer. Math. Soc., 176 (1973), 227–251 | DOI | MR | Zbl

[6] Khvedelidze B. V., “Metody integralov tipa Koshi v razryvnykh granichnykh zadachakh teorii golomorfnykh funktsii odnoi kompleksnoi peremennoi”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat., 7, M., 1975, 5–162 | Zbl

[7] Prësdorf Z., Nekotorye klassy singulyarnykh uravnenii, Mir, M., 1979

[8] Garnett Dzh., Ogranichennye analiticheskie funktsii, Mir, M., 1984 | Zbl

[9] Kazarian K. S., “Weighted norm inequalities for some classes of singular integrals”, Studia Math., 86 (1987), 97–130 | MR | Zbl

[10] Airapetyan G. M., “Zadacha Dirikhle v prostranstvakh s vesom”, Izv. NAN Armenii. Matem., 36:3 (2001), 12–35 | MR

[11] Airapetyan G. M., “O zadache Dirikhle v poluploskosti v prostranstvakh s vesom”, Izv. NAN Armenii. Matem., 36:6 (2001), 7–15 | MR

[12] Airapetyan G. M., “O zadache Gilberta v smysle $L^p$-skhodimosti, $p>1$”, Dokl. RAN, 328:4 (1993), 421–423 | MR | Zbl

[13] Seneta E., Pravilno menyayuschiesya funktsii, Nauka, M., 1985 | Zbl