$B-$Fractional Integrals on Variable Lebesgue Spaces

Abstract

Here, the fractional integral operators which are generated by Laplace-Bessel differential operator will be examined. It will also be shown that $M^{\alpha}_{\nu},\, I^{\alpha}_{\nu}: L_{p(\cdot),\nu}(\mathbb{R}^{n}_{k,+})\rightarrow L_{q(\cdot),\nu}(\mathbb{R}^{n}_{k,+})$ are bounded, where $M^{\alpha}_{\nu}$ is $B-$fractional maximal operator, $I^{\alpha}_{\nu}$ is $B-$Riesz potential and $\dfrac{1}{p(\cdot)}-\dfrac{1}{q(\cdot)}=\dfrac{\alpha}{Q}$.