This article is cited in 5 papers

Zygmund-type estimates for fractional integration and differentiation operators of variable order

B. G. Vakulov^a, E. S. Kochurov^a, N. G. Samko<sup>b

a</sup> Chair of Differential and Integral Equations, Southern Federal University, Rostov-on-Don, Russia
^b Center of Functional Analysis and Applications, University of Algarve, Faro, Portugal

Abstract: 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.

UDC: 517.518

Received: 30.12.2009

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:6, 20–28

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