Geodesic
Fractional Integrals of Imaginary Order in the Space of Hölder Functions with Polynomial Weight on an Interval
Matematičeskie zametki, Tome 74 (2003) no. 1, pp. 52-59 
N. K. Karapetyants; L. D. Shankishvili. Fractional Integrals of Imaginary Order in the Space of Hölder Functions with Polynomial Weight on an Interval. Matematičeskie zametki, Tome 74 (2003) no. 1, pp. 52-59. http://geodesic.mathdoc.fr/item/MZM_2003_74_1_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study fractional integrals of imaginary order in the Marchaud form in Hölder space with polynomial weight at finitely many points in the closed interval $[0,1]$. We present conditions on the orders of the weight for which this operator is invertible in the space described above.

[1] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Minsk, 1987

[2] Rubin B. S., “Drobnye integraly v prostranstvakh Gëldera s vesom i operatory tipa potentsiala”, Izv. AN ArmSSR. Matem., 3:4 (1974), 308–324

[3] Samko S. G., Murdaev Kh. M., Deistvie drobnogo integrodifferentsirovaniya v vesovykh obobschennykh prostranstvakh Gëldera $H_0^\omega(\rho)$ s vesom $\rho(x)=(x-a)^\mu(b-x)^\nu$, Dep. v VINITI 11.05.86. No. 3350, Rostov-na-Donu, 1986

[4] Murdaev Kh. M., Otsenka modulya nepreryvnosti integralov i proizvodnykh drobnogo poryadka, Dep. v VINITI 14.06.85. No. 4209, Groznyi, 1985

[5] Samko S. G., Murdaev Kh. M., “Vesovye otsenki Zigmunda dlya drobnogo differentsirovaniya i integrirovaniya i ikh prilozheniya”, Tr. MIAN SSSR, 180, Nauka, M., 1987, 197–198

[6] Karapetyants N. K., Murdaev Kh. M., Yakubov A. Ya., “Ob izomorfizme, osuschestvlyaemom drobnymi integralami v obobschennykh klassakh Gëldera”, Dokl. AN SSSR, 314:2 (1990), 288–291 | Zbl

[7] Karapetyants N. K., Murdaev Kh. M., Yakubov A. Ya., “Ob izomorfizme, osuschestvlyaemom drobnymi integralami v obobschennykh klassakh Nikolskogo”, Izv. vuzov. Matem., 1992, no. 9, 49–58

[8] Rubin B., “Fractional Integrals and Potentials”, Pitman Monographs and Surveys in Pure and Appl. Math., 82, 1996, 409 pp. | Zbl

[9] Karapetyants N. K., Shankishvili L. D., “Drobnye integraly i proizvodnye mnimogo poryadka”, Prikladnaya matematika i matematicheskoe modelirovanie, Feodosiya, 1997, 77–80

[10] Krein S. G., Petunin Yu. I., Semenov Ya. M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1978

[11] Karapetyants N. K., Yakubov A. Ya., “Uravnenie svertki so stepennoi nelineinostyu otritsatelnogo poryadka”, Dokl. AN SSSR, 320:4 (1991), 777–780 | Zbl

[12] Yakubov A., Shankishvili L. D., “Some inequalities for convolution integral transforms”, Integral Transforms and Special Functions, 2:1 (1994), 65–76 | DOI | MR | Zbl

[13] Karapetyants N. K., Shankishvili L. D., “Zamechanie o plotnykh mnozhestvakh v obobschennykh gelderovskikh klassakh”, Integro-differentsialnye operatory i ikh prilozheniya, no. 3, Rostov-na-Donu, 1998, 67–70