International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 777-788

Fractional integration operator of variable order in the holder spaces Hλ(x)

Bertram Ross1 and Stefan Samko2,3

1University of New Haven, 300 Orange Avenue, West Haven 06516, CT, USA
2Rostov State University, 105, Bol'shaya Sadovaya, Rostov-on-Don 344711, Russia
3Fulbright Scholar at the University of New Haven, USA

Received 17 June 1993; Revised 20 September 1993

Copyright © 1995 Bertram Ross and Stefan Samko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The fractional integrals Ia+α(x)φ of variable order α(x) are considered. A theorem on mapping properties of Ia+α(x)φ in Holder-type spaces Hλ(x) is proved, this being a generalization of the well known Hardy-Littlewood theorem.