The Riesz potential operator of variable order is shown to be bounded from the Lebesgue space with variable exponent into the weighted space , where with some and when is not necessarily constant at infinity. It is assumed that the exponent satisfies the logarithmic continuity condition both locally and at infinity and .
Cite this article
Vakhtang Kokilashvili, Stefan Samko, On Sobolev Theorem for Riesz-Type Potentials in Lebesgue Spaces with Variable Exponent. Z. Anal. Anwend. 22 (2003), no. 4, pp. 899–910DOI 10.4171/ZAA/1178