Geodesic
Singular integral equations on non-smooth curves in H\"older--Frech\'et space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2018), pp. 29-33.

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

We consider singular integral equations on non-smooth rectifiable curves and on certain classes of curves of infinite length.
Keywords: singular integral equation, non-smooth curve, Hölder condition
Mots-clés : Frechét space. 
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     title = {Singular integral equations on non-smooth curves in {H\"older--Frech\'et} space},
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B. A. Kats; S. R. Mironova; A. Yu. Pogodina. Singular integral equations on non-smooth curves in H\"older--Frech\'et space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2018), pp. 29-33. http://geodesic.mathdoc.fr/item/IVM_2018_10_a2/

[1] Muskhelishvili H. I., Singulyarnye integralnye uravneniya, Nauka, M., 1962

[2] Gakhov F. D., Kraevye zadachi, Nauka, M., 1977

[3] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, GITTL, M., 1950 | MR

[4] Dynkin E. M., “Gladkost integrala tipa Koshi.”, Zap. nauchn. semin. LOMI AN SSSR, 92, 1979, 115–133 | Zbl

[5] Salimov T., “Pryamaya otsenka singulyarnogo integrala Koshi po zamknutoi krivoi”, Nauchn. tr. MV i SSO Azerb. SSR, 5 (1979), 59–75

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

[7] Vekua I. N., Obobschennye analiticheskie fuktsii, Nauka, M., 1988

[8] Gorin S. V., “Ob odnoi algebre singulyarnykh operatorov v prostranstve gladkikh funktsii”, Izv. vuzov. Sev.-Kavkazsk. region. Ser. Estestven. nauki, 2006, no. 1, 11–15

[9] Kats D. B., “O nekotorykh novykh metricheskikh kharakteristikakh nespryamlyaemykh krivykh i ikh prilozheniyakh”, Tr. matem. tsentra im. N.I. Lobachevskogo, 46, 2013, 235–236

[10] Kats D. B., “Pokazateli Martsinkevicha i ikh prilozheniya v kraevykh zadachakh”, Izv. vuz. Matem., 2014, no. 3, 68–71

[11] Katz D. B., “Local and weighted Marcinkiewicz exponents with applications”, J. Math. Anal. Appl., 440:1 (2016), 74–85 | DOI | MR | Zbl

[12] Falconer K. J., Fractal geometry, 3rd Ed., Wiley and Sons, 2014 | MR | Zbl

[13] Kats B. A., “Zadacha Rimana na zamknutoi zhordanovoi krivoi”, Izv. vuzov. Matem., 1983, no. 4, 68–80

[14] Kats B. A., “The Riemann boundary value problem on non-rectifiable curves and related questions”, Complex Var. and Elliptic Equat., 59:8 (2014), 1053–1069 | DOI | MR | Zbl