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

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.

Keywords

• fractional integration
• variable fractional order
• mapping properties
• Holder continuous functions
• Hardy-Littlewood theorem.