Voir la notice de l'article provenant de la source Math-Net.Ru
@article{IVM_2003_2_a0, author = {B. G. Vakulov and N. K. Karapetyants and L. D. Shankishvili}, title = {Spherical convolution operators with a power-logarithmic kernel in generalized {H\"older} spaces}, journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika}, pages = {3--14}, publisher = {mathdoc}, number = {2}, year = {2003}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/IVM_2003_2_a0/} }
TY - JOUR AU - B. G. Vakulov AU - N. K. Karapetyants AU - L. D. Shankishvili TI - Spherical convolution operators with a power-logarithmic kernel in generalized H\"older spaces JO - Izvestiâ vysših učebnyh zavedenij. Matematika PY - 2003 SP - 3 EP - 14 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IVM_2003_2_a0/ LA - ru ID - IVM_2003_2_a0 ER -
%0 Journal Article %A B. G. Vakulov %A N. K. Karapetyants %A L. D. Shankishvili %T Spherical convolution operators with a power-logarithmic kernel in generalized H\"older spaces %J Izvestiâ vysših učebnyh zavedenij. Matematika %D 2003 %P 3-14 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/IVM_2003_2_a0/ %G ru %F IVM_2003_2_a0
B. G. Vakulov; N. K. Karapetyants; L. D. Shankishvili. Spherical convolution operators with a power-logarithmic kernel in generalized H\"older spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2003), pp. 3-14. http://geodesic.mathdoc.fr/item/IVM_2003_2_a0/
[1] Vakulov B. G., Operatory tipa potentsiala na sfere v obobschennykh prostranstvakh Gëldera, Dep. v VINITI 6.03.86, No 1553-B, Rostovsk. gos. un-t, Rostov, 1986, 31 pp.
[2] Vakulov B. G., “Operatory tipa potentsiala v obobschennykh klassakh Gëldera”, Izv. vuzov. Matematika, 1986, no. 11, 66–69 | MR | Zbl
[3] Vakulov B. G., “Sfericheskie operatory tipa potentsiala v obobschennykh prostranstvakh Gëldera s vesom na sfere”, Izv. vuzov. Sev.-Kavk. Region. Estestv. nauki, 1999, no. 4, 5–10 | MR | Zbl
[4] Samko S. G., “Singulyarnye integraly po sfere i postroenie kharakteristiki po simvolu”, Izv. vuzov. Matematika, 1983, no. 4, 28–42 | MR | Zbl
[5] Samko S. G., Gipersingulyarnye integraly i ikh prilozheniya, Izd-vo RGU, Rostov-na-Donu, 1984, 208 pp. | MR | Zbl
[6] Pavlov P. M., Samko S. G., “Opisanie prostranstv $L_p^\alpha(S_{n-1})$ v terminakh gipersingulyarnykh integralov”, DAN SSSR, 276:3 (1984), 546–550 | MR
[7] Vakulov B. G., Karapetyants N. K., Shankishvili L. D., “Sfericheskie potentsialy kompleksnogo poryadka v obobschennykh prostranstvakh Gëldera s vesom”, Dokl. RAN, 382:3 (2002), 301–304
[8] Vakulov B. G., Karapetiants N. K., Shankishvili L. D., “Spherical hypersingular operators of imaginary order and their multipliers”, Frac. Calculus and Apll. Anal., 4:1 (2001), 101–112 | MR | Zbl
[9] Kilbas A. A., “Stepenno-logarifmicheskie integraly v prostranstvakh gëlderovskikh funktsii”, Izv. AN BSSR. Ser. fiz.-matem. nauk, 1975, no. 1, 37–43 | MR | Zbl
[10] Kilbas A. A., “Operatory tipa potentsiala so stepenno-logarifmicheskimi yadrami v prostranstvakh Gëldera s vesom”, Izv. AN BSSR. Ser. fiz.-matem. nauk, 1978, no. 2, 29–37 | MR | Zbl
[11] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Navuka i tekhnika, Minsk, 1987, 688 pp. | MR
[12] Kilbas A. A., Saigo M., Bubakar S., “Sygmund type estimates and mapping properties of operators with power-logarithmic kernels in generalized Hölder spaces”, Math. Japonica, 40:3 (1994), 473–485 | MR | Zbl
[13] Samko S. G., Mussalaeva Z. U., “Fractional type operators in weighted generalized Hölder spaces”, Proc. Georgian Acad. Sci. Math., 1:5 (1993), 601–626 | MR
[14] Karapetyants N. K., Mussalaeva Z. U., “O razreshimosti integralnogo uravneniya drobnogo poryadka v obobschennykh gëlderovskikh prostranstvakh”, Differents. uravneniya, 32:8 (1996), 1102–1109 | MR | Zbl
[15] Vakulov B. G., Shankishvili L. D., Operatory so stepenno-logarifmicheskim yadrom v obobschennykh prostranstvakh Gëldera, Dep. v VINITI 17.03.99, No 819-V99, Rostovsk. gos. un-t, Rostov, 1999, 28 pp.
[16] Samko S. G., Vakulov B. G., “On equivalent norms in fractional order functions on a sphere”, Frac. Calculus and Apll. Anal., 3:4 (2000), 401–433 | MR | Zbl
[17] Samko S., Hypersingular integrals and their applications, Analytic methods and special functions, 5, Taylor and Francis, London–New York, 2002, 378 pp. | MR | Zbl
[18] Bari N. K., Stechkin S. B., “Nailuchshie priblizheniya i differentsialnye svoistva dvukh sopryazhennykh funktsii”, Tr. Mosk. matem. o-va, 5, 1956, 485–522 | MR
[19] Guseinov A. I., Mukhtarov Kh. Sh., Vvedenie v teoriyu nelineinykh singulyarnykh integralnykh uravnenii, Nauka, M., 1980, 415 pp. | MR
[20] Samko S. G., Murdaev Kh. M., “Vesovye otsenki Zigmunda dlya gipersingulyarnykh integralov”, Tr. MIAN SSSR, 180, 1987, 197–198
[21] Karapetiants N. K., Shankishvili L. D., “A short proof of Hardy–Littlewood type theorem for fractional integrals in Hölder spaces”, Fract. Calc. and Appl. Anal., 2:2 (1999), 177–192 | MR | Zbl
[22] Karapetyants N. K., Shankishvili L. D., “Drobnye integraly mnimogo poryadka v prostranstvakh Gëldera s vesom”, Dokl. RAN, 364:6 (1999), 738–740 | MR | Zbl