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CHOQUET INTEGRALS, HAUSDORFF CONTENT AND FRACTIONAL OPERATORS
Published online by Cambridge University Press: 19 March 2024
Abstract
We show that the fractional integral operator $I_{\alpha }$, $0<\alpha <n$, and the fractional maximal operator $M_{\alpha }$, $0\le \alpha <n$, are bounded on weak Choquet spaces with respect to Hausdorff content. We also investigate these operators on Choquet–Morrey spaces. The results for the fractional maximal operator $M_\alpha $ are extensions of the work of Tang [‘Choquet integrals, weighted Hausdorff content and maximal operators’, Georgian Math. J. 18(3) (2011), 587–596] and earlier work of Adams and Orobitg and Verdera. The results for the fractional integral operator $I_{\alpha }$ are essentially new.
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- Research Article
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- © The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
N.H. is financially supported by a Foundation of Research Fellows, The Mathematical Society of Japan. H.S. is supported by Grant-in-Aid for Young Scientists (19K14577), the Japan Society for the Promotion of Science. H.T. is supported by Grant-in-Aid for Scientific Research (C) (15K04918 and 19K03510), the Japan Society for the Promotion of Science.