The Boundedness of the Fractional Maximal Operator on Variable Lorentz-Karamata Spaces

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2026年4月13日

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Zhiwei Hao,
Ferenc Weisz

摘要

It turned out in recent papers that the fractional maximal operator $M_{\gamma ,s,\alpha }$ $M_{γ, s, α}$ has an important role in harmonic analysis. In this article, we prove that, under some conditions, $M_{\gamma ,s,\alpha }$ $M_{γ, s, α}$ 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_\alpha $ $M_{α}$ and $M_{\gamma ,s,\alpha }$ $M_{γ, s, α}$ on variable Lorentz-Karamata spaces are also discussed. Our results are new even for the classical fractional maximal operator.