Abstract It turned out in recent papers that the fractional maximal operator M, ₒ, M γ, s, α has an important role in harmonic analysis. In this article, we prove that, under some conditions, M, ₒ, M γ, s, α is bounded from variable martingale Hardy-Lorentz spaces to variable Lorentz-Karamata spaces. As an application, the boundedness of the classical fractional maximal operator M_ M α and M, ₒ, M γ, s, α on variable Lorentz-Karamata spaces are also discussed. Our results are new even for the classical fractional maximal operator.
Hao et al. (Wed,) studied this question.