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Variable Fofana's Spaces and Their Pre-Dual

School of Mathematics and System Sciences, Xinjiang University, Urumqi Xinjiang 830017, China
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Abstract

By introducing variable Fofana's spaces (Lp(·),Lq)α( ℝn)(1<p(·)<∞, 1≤q,α≤∞) and their pre-dual spaces, we discussed the properties of those spaces. Meanwhile, via applying hierarchical decomposition of function and real variable techniques, the necessary and sufficient conditions for boundedness of fractional integral operators and their commutators on variable Fofana's spaces are obtained.

Keywords

Fofana's spacesvariable exponentfractional integral operatorsBMOcommutators
CLC number: O174.2 Document code: A Article ID: 2096-7675(2023)05-0565-017

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Journal of Xinjiang University(Natural Science Edition in Chinese and English)
Volume 40 Issue 5,
September 2023
Pages 565-581
DOI: 10.13568/j.cnki.651094.651316.2023.01.19.0001

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Cite this article:
YANG F, ZHOU J. Variable Fofana's Spaces and Their Pre-Dual. Journal of Xinjiang University(Natural Science Edition in Chinese and English), 2023, 40(5): 565-581. https://doi.org/10.13568/j.cnki.651094.651316.2023.01.19.0001

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Received: 19 January 2023
Published: 01 September 2023
© 2023 Journal of Xinjiang University (Natural Science Edition in Chinese and English)