$B-$Fractional Integrals on Variable Lebesgue Spaces

Year 2024, Volume: 16 Issue: 2, 333 - 345, 31.12.2024

Esra Kaya

https://doi.org/10.47000/tjmcs.1505489

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 $\dfrac{1}{p(\cdot)}-\dfrac{1}{q(\cdot)}=\dfrac{\alpha}{Q}$.

Keywords

Fractional maximal operator, generalized translation operator, Riesz potential, variable Lebesgue space

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