International Journal of Mathematics and Mathematical Sciences 
Volume 18 (1995), Issue 4, Pages 777-788
doi:10.1155/S0161171295001001

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

Abstract

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.