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