Geodesic
Fractional integrals and differentials of variable order in Hölder spaces $H^{\omega(t,x)}$
Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 4, pp. 3-11 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider generalized Hölder spaces of functions on the segment of real axis, whose local continuity modulus has a dominant which may vary from a point to point. We establish theorems on the mapping properties of fractional integrals of variable order, from such a variable generalized Hölder space to another one with a “better” dominant, and similar mapping properties of fractional differentials of variable order from such a space into the space with “worse” dominant. Variable order can take values between zero and unity. 
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B. G. Vakulov; E. S. Kochurov. Fractional integrals and differentials of variable order in Hölder spaces $H^{\omega(t,x)}$. Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 4, pp. 3-11. http://geodesic.mathdoc.fr/item/VMJ_2010_12_4_a0/

[1] Bari N. K., Stechkin S. B., “Nailuchshie priblizheniya i differentsialnye svoistva dvukh sopryazhennykh funktsii”, Tr. Mosk. mat. obschestva, 5, 1956, 483–522 | MR | Zbl

[2] Vakulov B. G., “Sfericheskie potentsialy v vesovykh prostranstvakh Gëldera peremennogo poryadka”, Dokl. AN, 400:1 (2005), 7–10 | MR

[3] Vakulov B. G., “Sfericheskie operatory tipa potentsiala v vesovykh prostranstvakh Gëldera peremennogo poryadka”, Vladikavk. mat. zhurn., 7:2 (2005), 26–40 | MR | Zbl

[4] Vakulov B. G., “Operatory sfericheskoi svertki so stepenno-logarifmicheskim yadrom v prostranstvakh obobschennoi peremennoi gëlderovosti”, Izv. vuzov Sev.-Kavk. reg. Estestv. nauki, 2006, no. 1, 7–10 | Zbl

[5] Vakulov B. G., “Operatory sfericheskoi svertki v prostranstvakh peremennoi gëlderovosti”, Mat. zametki, 80:5 (2006), 683–695 | DOI | MR | Zbl

[6] Vakulov B. G., Samko N. G., Samko S. G., “Operatory tipa potentsiala i gipersingulyarnye integraly v prostranstvakh Gëldera peremennogo poryadka na odnorodnykh prostranstvakh”, Izv. vuzov. Sev.-Kavk. reg. Estestv. nauki. Aktualnye problemy mat. gidrodinamiki, 2009, Spetsvypusk, 40–45

[7] Ginzburg A. I., Karapetyants N. K., “Drobnoe integrodifferentsirovanie v gëlderovskikh klassakh peremennogo poryadka”, Dokl. AN, 339:4 (1994), 439–441 | Zbl

[8] Guseinov A. I., Mukhtarov Kh. Sh., Vvedenie v teoriyu nelineinykh singulyarnykh uravnenii, Nauka, M., 1980, 416 pp. | MR

[9] Karapetyants N. K., Ginzburg A. I., “Fractional integrodifferentiation in Holder classes of arbitrary order”, Georg. Math. J., 2:2 (1995), 141–150 | DOI | MR | Zbl

[10] Karapetyants N. K., Samko N. G., “Weighted theorems on fractional integrals in the generalized Holder spaces $H_0^w(\varrho)$ via the indices $m_w$ and $M_w$”, Fract. Calc. Appl. Anal., 7:4 (2004), 437–458 | MR | Zbl

[11] Ross B., Samko S. G., “Fractional integration operator of variable order in the Holder spaces $H^{\lambda(x)}$”, Intern. J. Math. and Math. Sci., 18:4 (1995), 777–788 | DOI | MR | Zbl

[12] Samko S. G., “Differentiation and integration of variable order and the Spaces $L^{p(x)}$”, Contemporary Math., 212 (1998), 203–219 | DOI | MR | Zbl

[13] Samko S. G., Murdaev Kh. M., “Weighted Zygmund estimates for fractional differentiation and integration, and their applications”, Proceedings of the Steklov Institute of Math., 3, 1989(180), 233–235 | Zbl

[14] Vakulov B. G., “Spherical potentials of complex order in the variable Holder spaces”, Integral Trans. and Spec. Funct., 16:5–6 (2005), 489–497 | DOI | MR | Zbl