Geodesic
Zygmund-type estimates for fractional integration and differentiation operators of variable order
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2011), pp. 25-34

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We consider non-standard generalized Hölder spaces of functions defined on a segment of the real axis, whose local continuity modulus has a majorant varying from point to point. We establish some properties of fractional integration operators of variable order acting from variable generalized Hölder spaces to those with a “better” majorant, as well as properties of fractional differentiation operators of variable order acting from the same spaces to those with a “worse” majorant.
Keywords: fractional integration operators, fractional differentiation operators, generalized continuity modulus, generalized Hölder spaces. 
@article{IVM_2011_6_a3,
     author = {B. G. Vakulov and E. S. Kochurov and N. G. Samko},
     title = {Zygmund-type estimates for fractional integration and differentiation operators of variable order},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {25--34},
     publisher = {mathdoc},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_6_a3/}
}
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B. G. Vakulov; E. S. Kochurov; N. G. Samko. Zygmund-type estimates for fractional integration and differentiation operators of variable order. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2011), pp. 25-34. http://geodesic.mathdoc.fr/item/IVM_2011_6_a3/