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Fractional Integration on Mixed Norm Spaces. II

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Abstract

In a previous paper Guo et al. (Fractional integration on mixed norm spaces. I. Preprint, 2022), we characterized the boundedness of fractional integration operators between mixed norm spaces over the unit disk. In this paper, we characterize the boundedness between X and Y, where

$$\begin{aligned} \begin{aligned} X, Y \in \{ H^p \ (0<p<\infty ),\ H^\infty ,\ \text {BMOA}, \ \mathcal {B}, \ H(p,q,\alpha ) \}. \end{aligned} \end{aligned}$$

As in Guo et al. (Fractional integration on mixed norm spaces. I. Preprint, 2022), we cover three types of fractional integration: Flett, Hadamard, and Riemann-Liouville, and we consider complex orders \(t \in \mathbb {C}\) instead of mere \(t \in \mathbb {R}\). Our findings provide, in particular, a complete answer to a problem started by Flett in 1972 (Theorem C).

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Acknowledgements

Fang is supported by Ministry of Science and Technology (Taiwan) (MOST) (108-2628-M-008-003-MY4). Hou is supported by National Natural Science Foundation (NNSF) of China (Grant No. 11971340).

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Authors and Affiliations

  1. School of Mathematics Science, Soochow University, Suzhou, 215006, People’s Republic of China

    Xiaolin Zhu, Feng Guo & Shengzhao Hou

  2. Department of Mathematics, National Central University, Chungli, Taiwan, ROC

    Xiang Fang

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  1. Xiaolin Zhu
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Zhu, X., Fang, X., Guo, F. et al. Fractional Integration on Mixed Norm Spaces. II. J Geom Anal 33, 158 (2023). https://doi.org/10.1007/s12220-023-01213-0

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