Abstract
In 2011, Dekel et al. introduced a highly geometric Hardy spaces \(H^p(\Theta)\), for the full range \(0<p\le 1\), which are constructed over a continuous multilevel ellipsoid cover \(\Theta\) of \(\mathbb{R}^n\) with high anisotropy in the sense that the ellipsoids can change shape rapidly from point to point and from level to level. We introduce a new class of fractional integral operators \(T_{\alpha}\) adapted to ellipsoid cover \(\Theta\) and obtained their boundedness from \(H^p(\Theta)\) to \(H^q(\Theta)\) and from \(H^p(\Theta)\) to \(L^q(\mathbb{R}^n)\), where \(\frac{1}{q}=\frac{1}{p}+\alpha\) and \(0<\alpha<1\).
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The authors express their thanks to the referees for valuable advice regarding a previous version of this paper.
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Baode Li is supported by the National Natural Science Foundation of China (Grant No. 12261083) and the Xinjiang Training of Innovative Personnel Natural Science Foundation of China (Grant No. 2020D01C048).
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Li, B.D., Sun, J.W. & Yang, Z.Z. Variable anisotropic fractional integral operators. Acta Math. Hungar. 170, 483–498 (2023). https://doi.org/10.1007/s10474-023-01368-w
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DOI: https://doi.org/10.1007/s10474-023-01368-w